Research ArticleA Cost Function Approach to the Prediction of PassengerDistribution at the Subway Platform

Xiaoxia Yang 1 Xiaoli Yang2 Zhenling Wang1 and Yuanlei Kang3

1 Institute of Complexity Science Qingdao University Qingdao 266071 China2College of Management and Economics Tianjin University Tianjin 264670 China3CRRC Qingdao Sifang CO LTD Qingdao 266111 China

Correspondence should be addressed to Xiaoxia Yang yangxiaoxiaqdueducn

Received 16 April 2018 Accepted 10 September 2018 Published 1 October 2018

Academic Editor Juan C Cano

Copyright copy 2018 Xiaoxia Yang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposes a cost function approach to predict the passenger distribution at the platform which is contributed to provideservices to the passenger safety and convenience and also an efficient use of the subway platform According to the limitedobservation andfield data collection of BeijingXuanwumen subway station passenger behaviors and basic attributes at the platformare analyzed Based on the analysis and investigation factors including the distance to the waiting area the passenger density inthe visual field and the length of the waiting area occupied by passengers are put forward as important factors to affect the choiceof the waiting area The determination of the real-time choice defined by these factors is applied to model the passengersrsquo waitingarea choice behaviors Simulation experiments are run for the model calibration and validation combining with the collected fielddata The results show that the passenger distribution which arises from the model is capable of keeping consistent with the actualdistribution in the rough The model is helpful for controlling how heavy carriages are congested and providing suggestions tooptimize the layout of platform facilities

1 Introduction

In most cities subways have contributed to the reductionof surface traffic and a better utilization of land resourcesHowever they have given rise to complex passenger flowsdue to complex station geometries that are most pronouncedduring peak hours The passenger dynamics relates to notonly physical characteristics but also behavior habits [1] Dur-ing the last few decades the interest in passengerpedestriandynamics has increased significantly for researchers fromphysics psychology computer science etc [2ndash5] So farresearch on passengerpedestrian dynamics at public placesmainly involves modeling fundamental diagram behaviorcharacteristics evacuation dynamics route choice etc

Pedestrian modeling methods are basically investigatedfrom both the microscopic level and the macroscopic level[6ndash8] The microscopic pedestrian model mainly containsthe cellular automata model [9ndash12] the social force model(SFM) [13 14] the agent-based model [15 16] and the gametheory model [17 18] The microscopic cellular automata

model is a grid-based discrete model [19] which is moresuitable for pedestrian dynamics in the complex environmentbecause of its simplicity and efficiency [20 21] The socialforce model is a continuous force-driven model and its firstapplication mainly focused on emergency evacuation frombuildings [22 23] The agent-based model usually uses thevirtual agents to develop the social structure it provides aninnovative perspective to study pedestrian dynamics [24]Manley et al [25] presented an agent-based model thatcan determine effects of changing the built environment onthe overall evacuation time of passengers The macroscopicpedestrian model focuses on studying the whole movingtrend of the crowd described by the average speed densitylocation and time The typical macroscopic model usuallymeans the fluid dynamic model which treats the pedestrianflow as fluid or gas [26 27] Applications of the pedestriansimulations prompted a number of commercial evacuationsoftware programs such as EGRESS EXODUS SIMULEXEXITT WAYOUT FDS+Evac etc [28 29]

HindawiJournal of Advanced TransportationVolume 2018 Article ID 5031940 15 pageshttpsdoiorg10115520185031940

2 Journal of Advanced Transportation

Dwell time Separation time

Cycle c Cycle c+1Cycle c-1 Cycle c+2

t

ak Arrival time of train k dk Departure time of train k

ak ak+1dk dk+1dk-1 ak+2

Figure 1 The diagram of a cycle

Generally the validity of a pedestrian model is obtainedby comparing the simulation results with the fundamentaldiagrams Based on the field observation some character-istics of walking behaviors are found and also representedby pedestrian models such as the typical self-organizationphenomenawhich refer to lane formation in the bidirectionalflow [30] strips in the crossing flow [31] and ldquozipperrdquo effectsEnsuring the safety of evacuation has been an importantfactor during the design of public infrastructure [32] Pedes-trian models have been applied to investigate evacuationproblems from different perspectives such as computingevacuation time and finding evacuation bottlenecks [33]Route choice not only has a direct effect on trying to stayaway from congested routs but also affects the evacuationtime significantly [34]

Platform as an important part of rail transport usuallyhas a relatively large and complicated passenger flow Pas-senger behaviors at the subway platform consist of walkingwaiting area choice waiting for a train and alighting andboarding Much research has been done on alighting andboarding behaviors from data statistic and modeling as wellas the study on walking behaviors [35] Zhang et al presenteda cellular automata-based alighting and boarding model tocapture the fundamental traits of alighting and boardingbehaviors [35] Seriani and Fernandez proposed a methodto determine the effect of passenger traffic management inthe alighting and boarding time by means of simulations andexperiments [36]Wu andMa introduced a new classificationmethod of the crowdedness level at the platform consideringpassenger flow characteristics and boarding services [37]Johansson et al studied the waiting behaviors based on theSFM by introducing a series of extensions [22] Basicallypassenger distribution at the platform resulting from thewaiting area choice behavior directly affects the congestiondegree in carriages the research on which can providesuggestions to optimize the layout of the platform facilitiesand thereby adjust passenger distributions However as theprocess of waiting area choice is chaotic modeling this choicebehavior is full of uncertain factors beyond our knowledge

Existing studies on the waiting area choice behaviorsare still comparatively few [38 39] because a lot of inves-tigation labor and time are required during the field datacollection [40] According to Szplett and Wirasinghe [41]the distribution of passengers at a platform is not uniformand changes with time Wu et al proposed a passengerdistribution model based on the potential energy functionfor waiting areas [38] However the random characteristicsof passenger distribution at the platform and also the detailed

passenger walking dynamics of choosing a waiting area arenot considered The main contribution of this paper is thatthe proposed model combines the real-time distribution ofpassengers at the platform with the microscopic passengermovement dynamics for improving the simulation authen-ticity and accuracy Given the initial passenger distributionat the platform and the traffic inflow the proposed model canexhibit the behaviors of passengersrsquo waiting area choice in realtime

Different pedestrian models provide different levels ofmodeling characteristics and details This paper chooses theSFM as the reference passenger driven model which can offera good performance of reflecting pedestrian behaviors sothe combination of the waiting area choice model and theSFM can be capable enough to depict passengersrsquo searchingbehaviors at the platform while at the same time alsoguaranteeing the accuracy

The structure of this paper is as follows Section 2proposes a cost function approach to predict passenger dis-tribution at the platform in which the distance to the waitingarea passenger density in the visual field the length of thewaiting area occupied by passengers and other factors are allconsidered Also the passenger driven model which refers tothe very frequently applied SFM is introduced Section 3 givespassengersrsquo basic attributes at Beijing Xuanwumen subwaystation and calibrates and validates the proposed modelin this paper based on the limited observation and fielddata at Beijing Xuanwumen subway station and Shanghainatural history museum station Section 4 reviews the keydiscoveries

2 Model

In this section we define a cycle as the time gap between anarrival of two successive trains shown in Figure 1 Duringa cycle the total time gap can be divided into dwell timeand separation time of the train ldquokrdquo before an arrival of thenext train ldquo119896 + 1rdquo Passenger behaviors such as searchingbehaviors waiting behaviors and alighting and boardingbehaviors occur in each cycle When passengers enter theplatform during the separation time they will first beginsearching for a relatively appropriatewaiting areawhich is notonlywithin an acceptable range but also not very crowded yetthen waiting behaviors and alighting and boarding behaviorswill occur When passengers enter the platform during thedwell time waiting behaviors may not be required if there isenough time for boarding and also enough space inside ofthe corresponding carriage According to Wu and Ma [42]

Journal of Advanced Transportation 3

WaitingareaCirculating

area

Figure 2 Waiting areas at the platform

a platform mainly consists of two areas shown in Figure 2circulating areas and waiting areas Both waiting behaviorsand alighting and boarding behaviors are mainly carried outin the waiting areas

Subway stations are mostly in a relatively closed under-ground space and pedestrians walking in these confinedspace often produce some different behavior habits fromwalking in the ordinary sidewalk Firstly passenger traffic atthe platform varies significantly with an arrival of a trainNote that passenger traffic here means the total number ofpassengers who may enter or leave the platform Passen-ger traffic is not continuously invariant but shows suddenincrease or sudden decrease especially during dwell time andthe initial stage of separation time The sudden change ofpassenger traffic relates to the location of a station time theweather condition large events etc The impact of a suddenincrease of passenger traffic on various facilities at the stationis very large especially around the stairescalator which mayfurther result in the formation of a security risk Secondlypassenger flow at the platform has the nonuniform charac-teristics in time and space During the morning and eveningpeak hours of workdays passenger traffic is particularly largewhich is several times higher than that at any other time ofa day Large differences in the passenger traffic for the areasof a platform with two different driving directions do existTake the platform of line 4 at Beijing Xuanwumen subwaystation for example passenger density at the platform withAnheqiao North direction which leads to the city center isobviously higher than that with the opposite direction duringthe morning rush hours while the situation is just reversedduring the evening rush hoursThis is because people mainlywork in the inner ring of the city and live in the suburbs

According to Hoogendoorn and Bovy [43] pedestrianbehavior has three levels which are respectively strategiclevel tactical level and operational level Passenger travelpurposes bonded groups etc at the platform are assumed tobe known in this paper which are all at the strategic levelThisdirectly determines which side of the platform passengerschoose Note that the platform could be with the islandtype or the side type When passengers enter the platformthe waiting area choice behavior affected by both personalfactors and external factors is at the tactical level this decision

is mostly performed after some time which is needed togather information This paper assumes that passengers canget information from time to time and could make quickdecisions once entering the platform The novel contributionof our paper is to present a waiting area choice model Theforce-driven equation for passengersrsquo walking in this paper isthe SFM [23] in which both physical and motivation forcesare considered this is thus at the operational level

21 Waiting Area Choice Model for Passengers Through alarge number of investigations at the subway platform andalso analyzing the video data we discover that waiting areachoice behavior for passengers is more likely to be affectedby the passenger density in the visual field the distance tothe waiting area a cycle at the dwell time or separation timelarge pieces of luggage and other uncertain factors Eachinfluence factor can result in generating a part of cost In thispaper we assume that a passenger makes continuous choicesaccording to the real-time situations and this decision-making considers all the above influence factors

This paper first puts forward the concept of the expectedcost 119862119894119908(119905 119909 119910) for the passenger 119894 in the position (119909 119910) tochoose a waiting area 119908 at time 119905 When determining whichwaiting area the choice is governed by the expected costwhich represents a possible minimum cost is an optimalwaiting area We express 119862119894119908(119905 119909 119910) as

119862119894119908 (119905 119909 119910) = 3sum119896=1

119862119894119908119896 (119905 119909 119910) + 120585 (1)

where 119862119894119908119896 (119905 119909 119910) is the expected cost caused by detailedfactors to affect the selection of waiting areas and 120585 is anuncertain cost caused by someother uncertain factors beyondour knowledge which fits the normal function

We introduce 1198621198941199081 1198621198941199082 and 1198621198941199083 as the expected costsresulting from the distance to the waiting area the lengthof the waiting area occupied by passengers and passengerdensity in the area from hisher current position to thecorresponding waiting area shown in Figure 3 respectively

We compute 1198621198941199081 as

1198621198941199081 (119905 119909 119910) = exp(1205721 sdot 119889119894119908 (119905 119909 119910) sdot 120583 (119905 119909 119910)1205731 ) (2)

We define 119889119894119908(119905 119909 119910) as the distance from passengerrsquoscurrent position (119909 119910) to the center point of the waiting area119908 at time 119905 The influence degree of 119889119894119908(119905 119909 119910) on the waitingarea choice can also be affected by the passenger densitynearby We hypothesize that variable 120583(119905 119909 119910) represents thisinfluence it is given by (3) It can be interpreted as followswhen passengers enter the platform from the stairescalatorand then observe a large number of pedestrians gathering inthe waiting areas which are near the stairescalator they mayprefer to choose a further waiting area

120583 (119905 119909 119910) =

1 if 120588 (119905 119909 119910) le 1205880120588 (119905 119909 119910)1205880 if 120588 (119905 119909 119910) gt 1205880 (3)

4 Journal of Advanced Transportation

w-1w-2

i

w+1w w+5w+2 w+3 w+4

j

i Sw

２n２

j

Figure 3 Illustration of passenger motions at the platform

10

9

8

7

6

5

4

3

2

1

y (m

)

2 4 6 8 10

x (m)

Rn

Figure 4 Illustration of density calculation using the Voronoidiagram

Table 1 Passenger density andmobility at different levels of service

Level of service Passenger density (pm2) Passenger mobilityA le 083 Not affectedB 083-111 Slightly affectedC 111-143 Affected evadeD 143-333 Severely restrictedE 333-50 stagnationF ge 50 stagnation

where 120588(119905 119909 119910) = 119873sum119873119894=1 |119860 119894| is the passenger densitynearby within the sector area with a radius 119877119899 and isillustrated in Figure 4 Note that the density is calculated bythe Voronoi diagram [44]119873 is the number of passengers inthe sector and 119860 119894 is the area of each Voronoi cell Actuallythe radius of a vision field 119877V is usually larger than 119877119899 Wehypothesize a central angle of 2120579 = 170∘ 1205880 is determinedaccording to the level of service [45] listed in Table 1 Inthis paper we assume 1205880 = 083 pm2 When 1205880 ge 083pm2 passengers will feel uncomfortable and their mobilitieswill be restricted severely at these areas At this time someevacuation strategies will be adopted at the platform forexample public broadcasting or staff guiding passengers tosomewhere with relatively few people as shown in Figure 5

Stationworker

Ourresearcher

Waiting passengers

Searching passengers

Figure 5 Station worker guides passengers to the middle part of theplatform

1205731 is a sensitive positive parameter for scaling theexpected cost 1198621198941199081 1205721 is an inertia positive parameter whichis affected by the passengerrsquos arriving time at the platform andwhether or not they are carrying large pieces of luggageThen1205721 is expressed by

1205721=

119863119879119879119871 if (119889119908119890119897119897 (119905) = 1 or 119897119906119892119892119886119892119890 (119905) = 1) and 119889119894119908 gt 11988901 if 119900119905ℎ119890119903119904

(4)

Here 119863119879means dwell time which is defined in Figure 1and 119879119871 refers to the time left in the dwell time period119889119908119890119897119897(119905) = 1 represents a cycle at the dwell time in timeinstant 119905 otherwise at the separation time 119897119906119892119892119886119892119890(119905) = 1represents the passenger carrying large pieces of luggageotherwise not carrying When passengers at somewhere ofthe platform are informed of the coming of a train theymay prefer to choose a nearby waiting area with relativelyfew people If passengers carry large pieces of luggage whichcan result in the walking speed reducing the distance factorwill be considered as a very important influence factor inthis paper and passenger would like to choose a nearerwaiting area In this paper we hypothesize that 1198890 is a positiveconstant

The number of passengers in the waiting area is anotherimportant factor to affect the decision-making reflectedby the variable 1198621198941199082 (119905 119909 119910) We define the expression of

Journal of Advanced Transportation 5

1198621198941199082 (119905 119909 119910) as a piecewise function according to a cycle atdifferent time levels it is given by

1198621198941199082 (119905 119909 119910)

=

1205732119871119908119886119891119905119890119903 (119905) + 1205722 1119871119908 minus 119871119908

119886119891119905119890119903 (119905) if 119889119908119890119897119897 (119905) = 11205732119871119908119887119890119891119900119903119890 (119905) + 1205722 1

119871119908 minus 119871119908119887119890119891119900119903119890 (119905) if 119889119908119890119897119897 (119905) = 0

(5)

119871119908119886119891119905119890119903(119905) and 119871119908119887119890119891119900119903119890(119905) are the length of the waiting areaoccupied by passengers at the dwell time and the separationtime respectively According to our observation the lengthof queue becomes shorter with an arrival of a train 119871119908 is thephysical length of the waiting area 119908 which is determinedaccording to the structure of the platform In this paperwe only consider the situation of 119871119908 ge 119871119908119886119891119905119890119903(119905) for thesubsequent model validation and calibration 1205732 is a sensitivepositive parameter for scaling 1205722 is an inertia positiveparameter which determines the attractive ability of the leftspace of a waiting area

In this paper 119871119908119886119891119905119890119903(119905) and 119871119908119887119890119891119900119903119890(119905) are given accordingto [42]

119871119908119886119891119905119890119903 (119905) = 0694119899119908 (119905)0510 119871119908119887119890119891119900119903119890 (119905) = 0685119899119908 (119905)0546

(6)

Here 119899119908(119905) denotes at the waiting area 119908 at time 119905The passenger density 120588119894119908(119905 119909 119910) in the area 119878119908 shown

in Figure 3 is another factor that needs to be considered Let1198621198941199083 (119905 119909 119910) denote this influence factor we define this factoras

1198621198941199083 (119905 119909 119910) = exp(120588119894119908 (119905 119909 119910)1205733 ) (7)

1205733 is a sensitive positive parameter for scaling theexpected cost 1198621198941199083 Basically the alighting passengers canleave the platform within a short time and therefore theyaffect the waiting area choice behaviors mostly concentratedin the start stage of the separation time

Therefore the optimal waiting area 119908lowast for the passenger119894 is given by

119908lowast = argmin119862119894119908 119908 = 1 2 3 119899 minus 1 119899 (8)

We define 119899 as the total number of waiting areas that isrelated to the physical structure of a platform

In this paper we assume that passenger determines anoptimal waiting area from time to time until his or herdistance to the optimal waiting area is less than a detectionthreshold Behavior like changing to another waiting areaduring boarding is not considered in this paper

22 Modeling Passenger Movement In this section we willgive a brief description of the passenger driven model basedon the SFM The SFM is proposed by Helbing et al [13 23]where pedestrians are driven by three types of forces the

desired force997888rarr1198910119894 the interaction force between pedestrians

119894 and 119895 997888rarr119891 119894119895 the interaction force between the pedestrian 119894and walls 119908 997888rarr119891 119894119908 The SFM has been a prevalent microscopicsimulation model in pedestrian dynamics and is still beinginvestigated and embedded into the numerical simulationsoftware such as Anylogic [46] and FDS+Evac [29] Someself-organization phenomena are also represented throughthe application of the SFM [47] which further reveals theusability of the model

The mathematical formula of the SFM is expressed by

119898119894119889997888rarrV 119894 (119905)119889119905 = 997888rarr1198910119894 + sum

119895( =119894)

997888rarr119891 119894119895 +sum119908

997888rarr119891 119894119908 (9)

where 119898119894 is the mass of pedestrian 119894 and 997888rarrV 119894(119905) is hisher

walking velocity at time 119905 997888rarr1198910119894 indicates the pedestrianrsquoswillingness to achieve the desired speed

At the subway station we can always observe the bondedgroups such as families friends colleagues and couplesespecially on the weekends This paper also considers theeffects of bonded groups based on the SFM and we directlyadopt the bonding force proposed in [1] which has alreadybeen calibrated and validated As bonded groups could bearthe shorter distance between each other because of theirspecial relationships the bonding force 119896119887119900119899119889119894119895 has the oppositedirection of the force 119891119894119895 The force-driven equation forpassengers in the bonded group is given by

119898119894119889997888rarrV 119894 (119905)119889119905 = 997888rarr1198910119894 + sum

119895( =119894)119895isin119861(119894)

997888rarr119891 119894119895 +sum119908

997888rarr119891 119894119908+ sum119895isin119861(119894)

(119896119887119900119899119889119894119895 + 119891119887119900119899119889119894119895 ) (10)

119891119887119900119899119889119894119895 is the interaction force between passengers 119894 and 119895who belong to the set of bonded groups 119861(119894) For passengersin the same bonded group we assume that they would choosethe same waiting area

It is easy for a pedestrian to vibrate continuously ina high density crowd especially when he or she is in thebottleneck area [48] Pelechano et al introduced a ldquostoppingrulerdquo to avoid this behavior where hisher own personalitythe walking directions of others and pedestrianrsquos currentsituation were all taken into account [48] Besides a ldquorespectrdquomechanism as a self-stopping mechanism was introduced byParisi et al which reproduced the experimental data and alsoavoided the vibration [49] In this paper we adopt the sameldquorespectrdquo mechanism in [49]The respect distance119863119877 for thepassenger 119894 is 119863119877119894 = 119877119865 sdot 119903119894 where 119877119865 is the respect factorOnce any other pedestrian touches the respect area of thepedestrian 119894 which is 120587 sdot 1198632119877119894 the desired walking speed V0119894will be set to 0 until the respect area is free In this paper it isalso assumed that 119877119865 = 07 and we refer the readers to [49]for more details

When passengers arrive at the target waiting area weassume they will queue up to two columns at the mark

6 Journal of Advanced Transportation

Start

Input parameters ofthe scenario and

passengers

Calculate the simulation time

Within separation time End

Movement based on the SFM

No

Yes

Yes

Compute a target waiting area

Change the targetwaiting area

Change the desired walking

Keep the previous desiredNo

based on wlowast

walking direction rarre 0i

direction rarre 0i

Figure 6 The flow diagram of the passenger movement process at the platform

insertions of the waiting area and the desired positions willrelate to 119871119908119886119891119905119890119903(119905) or 119871119908119887119890119891119900119903119890(119905) Moreover this paper mainlyfocuses on the waiting area choice behavior of passengers atthe tactical level and the alighting and boarding behaviorsare not investigated

23 Modeling of Passenger Distribution at the Platform Pas-senger distribution at the subway platform could be predictedby the combination of waiting area choice model and passen-ger driven model The target waiting area 119908lowast determined by(8) affects a passengerrsquos desired walking direction 997888rarr119890 0119894 in theSFM In particular the flowdiagramof themovement processof passengers at the platform is shown in Figure 6 and thedetailed description is given as follows

(1) Build the platform according to the CAD diagramGenerate passengers and populate them at the plat-formnear the stairsescalatorswith randompositions

Their initial speeds are set to be 1ms and the desiredwalking directions point to the front waiting areadirectly for simplicity The number of passengersgenerated is evenly distributed over time while boththe total number of passengers and the ratio of thepassenger quantity from the left stairsescalators tothat from the right are set according to the actualdemands

(2) Calculate the simulation time If the time lengthexceeds the separation time end the simulation

(3) Compute a target waiting area 119908lowast according to thechoice model proposed in this paper Determinewhether or not changing the target waiting area Ifthe passenger keeps the previous choice of the waitingarea keep the previous desired walking directionand update the position according to the SFM Elsechange the desired walking direction according to

Journal of Advanced Transportation 7

Line 4 Line 2

Figure 7 The location of Xuanwumen subway station in the Beijing subway system

the new target waiting area Then update the newposition according to the SFM

(4) For each passenger repeat step (3) until all passengersfinish their updating

(5) Repeat steps (2) (3) and (4) until reaching therequired simulation time

3 Case Study

31 Passengersrsquo Basic Attributes According to the statisticsBeijing metro network shown in Figure 7 now has 18 lines inoperation with a total length of over 550 km In accordancewith the current plan the mileage of Beijing metro will reach997km by 2020 In addition the carrying capacity of urbanrail transit increases year by year the daily passenger volumeof Beijing subway reaches over 10000000 The platformof line 4 of Beijing Xuanwumen subway station shown inFigure 8 is chosen as an investigation platform in this paperfor the observation and data collection Xuanwumen stationis an interchange station of line 2 and line 4 Ridership atXuanwumen station is very large especially during themorn-ing and evening peak hours According to the transportationexperience in Beijing 700-900 am and 1700-1900 pm are

rush hours while the other hours are all considered as off-peak hours

In this paper we choose P0 in Figure 8 as the observationplace to collect the data of passengersrsquo basic attributes from1800 pm to 2000 pmThe collected attributes mainly consistof male-to-female ratio age structure bonding rate andluggage statistics Some statistics data are listed in Table 2This table reflects that there is not any significant difference inthe gender ratio and most passengers are young and middle-aged for about 95 because of the complex structure of thestation and the existence of stairsescalators In additionthe bonding rate is around 10 and the ratio of passengerscarrying large pieces of luggage is around 5 Passengers whotake the large pieces of luggage always have the relatively lowtravel efficiency and they mainly transfer to Beijing SouthRailway StationThemasses of passengers are set according tothe statistics data fromNational Health and Family PlanningCommission of the Peoplersquos Republic of China Moreoverother data in Table 2 are consistent with that in [50]

There are stairsescalators on both sides of the platformthrough which passengers enter or leave the platform Thefield data of the inflow and outflow from 1830 pm to 2000pm are collected at the observation places P119897 and P119903 Thesoftware SPSS is applied to test the collected data for the

8 Journal of Advanced Transportation

StairEscalator

Toilet Monitoringroom

Distributionroom

Soil body

To Tiangongyuan

To Anheqiao North

Escalator

Stair

Escalator

24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

０l

０0

０r

Figure 8 The simplified 2D diagram of the platform of line 4 at Xuanwumen subway station

Table 2 Passengersrsquo basic attributes at the platform of line 4 of Xuanwumen subway station

Passenger category Young and middle-aged (Male) Young and middle-aged (Female) Child ElderlyAge 18le age lt 60 18le age lt60 agelt18 age ge 60Proportion () 475 48 31 14Mass (kg) 66 plusmn 15 57 plusmn 15 30 plusmn 15 65 plusmn 15Radius (m) 0270 plusmn 0020 0240 plusmn 0020 0210 plusmn 0015 0250 plusmn 0020Desired speed (ms) 135 plusmn 020 115 plusmn 020 090 plusmn 030 080 plusmn 030Reaction time (s) 1 plusmn 02 1 plusmn 02 1 plusmn 02 1 plusmn 02

statistically significant correlations The testing results showthat 1198681 sim N(85 36) 1198741 sim N(78 26) 1198682 sim N(76 28) and1198742 sim N(78 27) with a 5 significance level 1198681 and 1198741respectively denote the entering and leaving numbers ofpassengers from the observation place P119897 during a cycle1198682 and 1198742 are corresponding values from P119903 in a cyclerespectivelyThemean value of 1198681 is obviously larger than thatof 1198682 which could directly result in the difference in passengerdistribution at the platform During our simulation the ratioof inflow from P119897 to that from P119903 also keeps the same valuewith our field data

32 Model Calibration This paper focuses on investigatingpassengersrsquo waiting area choice behaviors and field dataat the platform with time is collected In each cycle timethe collected data mainly contain the number of alightingpassengers 119873119908119886119897119894119892ℎ119905 the number of passengers who could notboard the train for some reason in the previous cycle time119873119908119908119886119894119905 an increase in the number of waiting passengers duringthe time between the initial of a new cycle time and beinginformed of an arrival of a train 119873119908119887119890119891119900119903119890 and an increasein the number of passengers during the time between beinginformed of the coming of a train and the open of traindoors 119873119908119894119899119888119903119890119886119904119890 Therefore the total number of passengersbefore the open of train doors in each cycle time 119873119908119903119890119886119897 is119873119908119908119886119894119905 + 119873119908119887119890119891119900119903119890 + 119873119908119894119899119888119903119890119886119904119890 Note that the station staff alwaysbroadcast the coming of a train Once broadcasting startswe will record the required 119873119908119887119890119891119900119903119890 thereby According to theobservation and statistics one reason for not boarding maybe that the space in the train is not enough for the waitingpassengers another reasonmay be that the train does not passpassengersrsquo destination station because of the operationmodeof the long-short routing In this paper we do not considerthe strategic level of their destinations but regard the resultsof these passengersrsquo choices as input data

As mentioned above large difference in the passengertraffic for two different driving directions at the platform ofline 4 of Xuanwumen subway station exists In addition thetraffic of boarding passengers with Anheqiao North directionis not very large during the evening rush hours while thetraffic of alighting passengers is relatively large We chooseto use the field data of 119873119908119887119890119891119900119903119890 119873119908119894119899119888119903119890119886119904119890 119873119908119908119886119894119905 and 119873119908119886119897119894119892ℎ119905 ineach cycle during the time from 1830 pm to 1900 pm for 24waiting areas with Anheqiao North direction at Xuanwumensubway station and the mean values of the field data andtheir corresponding approximate integer values marked byldquoestimated mean valuerdquo are shown in Figures 9 10 and 11which also indicate the position of stairs Note that there isno passenger who could not board in the dwell time For ourstatistic data in each cycle time we can find the significantdifference between the total number of waiting passengerssum24119908=1119873119908119903119890119886119897 and the alighting passengers sum24119908=1119873119908119886119897119894119892ℎ119905 Thestatistic results indicate that the mean value of sum24119908=1119873119908119887119890119891119900119903119890during a cycle time is 36 with a standard deviation 9 and themean value of sum24119908=1119873119908119894119899119888119903119890119886119904119890 is 20 with a standard deviation3 while the mean value ofsum24119908=1119873119908119886119897119894119892ℎ119905 is 153 with a standarddeviation 29 These numerical fluctuations of sum24119908=1119873119908119887119890119891119900119903119890and sum24119908=1119873119908119894119899119888119903119890119886119904119890 are not very great which provide us thepossibility of calibrating the model based on these dataThough the statistic data of the number of passengers at eachwaiting area during each cycle time always vary randomlywithin a certain range the overall distribution is similar withmore passengers on both ends of the platform

According to statistics and timetable of trains traindeparture interval is 180 s during our investigation timefrom 1830 pm to 1900 pm with Anheqiao North directionGenerally the dwell time for each train ranges from 30 s to 45s and passengers are usually informed of the coming of a trainin advance through broadcasts and displayersWe assume the

Journal of Advanced Transportation 9

The mean number of passengers before the arrival of a train

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5

Figure 9The field number of passengers at eachwaiting area beforebeing informed of the arrival of a train119873119908119887119890119891119900119903119890 with Anheqiao Northdirection

An increase in the number of passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4

Figure 10 An increase in the field number of passengers at eachwaiting area119873119908119894119899119888119903119890119886119904119890 with Anheqiao North direction

longest time for passengers knowing the coming of a trainis 55 s For the feasibility of simulations the total numberof passengers with Anheqiao North direction in a cycle timeis 56 and sum24119908=1119873119908119886119897119894119892ℎ119905 = 153 during our simulation whichkeep the same with the mean field values among which thenumber of passengers coming from the left stairescalatoris 30 and 26 passengers are from the right stairescalatorAssume that passengersrsquo waiting area choice behaviors are notaffected by passengers with the other train driving directionin this paper

Basically parameter calibration of a model is very criticalto simulations [1] Parameters in the passenger driven modelof this paper have already been adapted in [1 23] whileparameter calibration in the waiting area choice model stillrequires further investigations As shown in Section 2 1198890 12057221205731 1205732 and 1205733 are the sensitivity parameters to be calibratedThe values of these parameters are related to the probabilityof choosing a waiting area Themethod of setting parameters

The number of alighting passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 11 The field number of alighting passengers at each waitingarea119873119908119886119897119894119892ℎ119905 with Anheqiao North direction

in this paper refers to [1] experiments with different values ofabove parameters are run for the investigation of the influenceof these sensitivity parameters associatedwith the perceptionof the simulation dynamics and actual observations at theplatform Meanwhile we propose to determine the aboveparameters based on the field data and the magnitudes of1198621198941199081 1198621198941199082 and 1198621198941199083 are recorded with the repeated numericalsimulations in order to regulate the influence degree ofdifferent factors Furthermore throughminimizing themeanerror E = (sum24119908=1 |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899|)24 the parameterscould be finally determined Among which119873119908119904119894119898119906119897119886119905119894119900119899 is thesimulation result of the number of passengers at each waitingarea before the opening of train doors

During the parameter calibration the mean values of thenumbers of passengers from the left and right stairsescalatorsin the simulation runs are set according to those in Figures 910 and 11 Considering all of the above criteria parameters inthis paper are set as 1198890 = 10 1205722 = 29 1205731 = 110 1205732 = 08and 1205733 = 100

After using the above parameters the dynamic char-acteristics for passengers when searching for the waitingareas could be found in the simulation snapshots shown inFigure 12 During the first few seconds of the separationtime alighting passengers occupy the main position at theplatform as shown in Figure 12(a) After that there arepassengers entering the platform continuously and choosingan appropriate waiting area as shown in Figures 12(b) and12(c) During our field observation stairs on both sides ofthe platform mainly serve outbound passengers during theinitial stage of the separation time so does the simulation InFigure 13 the box-plot shows the field number of passengersat each waiting area before the opening of doors during eachcycle time through statistics and also the simulation resultsof a random experiment marked with magenta asterisksNote that the central red mark in Figure 13 is the medianvalue of the field number of passengers at each waiting areaand the bottom and top edges of the blue box are the 25thand 75th percentiles of all collected field data respectively

10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

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Journal of Advanced Transportation 3

WaitingareaCirculating

area

Figure 2 Waiting areas at the platform

a platform mainly consists of two areas shown in Figure 2circulating areas and waiting areas Both waiting behaviorsand alighting and boarding behaviors are mainly carried outin the waiting areas

Subway stations are mostly in a relatively closed under-ground space and pedestrians walking in these confinedspace often produce some different behavior habits fromwalking in the ordinary sidewalk Firstly passenger traffic atthe platform varies significantly with an arrival of a trainNote that passenger traffic here means the total number ofpassengers who may enter or leave the platform Passen-ger traffic is not continuously invariant but shows suddenincrease or sudden decrease especially during dwell time andthe initial stage of separation time The sudden change ofpassenger traffic relates to the location of a station time theweather condition large events etc The impact of a suddenincrease of passenger traffic on various facilities at the stationis very large especially around the stairescalator which mayfurther result in the formation of a security risk Secondlypassenger flow at the platform has the nonuniform charac-teristics in time and space During the morning and eveningpeak hours of workdays passenger traffic is particularly largewhich is several times higher than that at any other time ofa day Large differences in the passenger traffic for the areasof a platform with two different driving directions do existTake the platform of line 4 at Beijing Xuanwumen subwaystation for example passenger density at the platform withAnheqiao North direction which leads to the city center isobviously higher than that with the opposite direction duringthe morning rush hours while the situation is just reversedduring the evening rush hoursThis is because people mainlywork in the inner ring of the city and live in the suburbs

According to Hoogendoorn and Bovy [43] pedestrianbehavior has three levels which are respectively strategiclevel tactical level and operational level Passenger travelpurposes bonded groups etc at the platform are assumed tobe known in this paper which are all at the strategic levelThisdirectly determines which side of the platform passengerschoose Note that the platform could be with the islandtype or the side type When passengers enter the platformthe waiting area choice behavior affected by both personalfactors and external factors is at the tactical level this decision

is mostly performed after some time which is needed togather information This paper assumes that passengers canget information from time to time and could make quickdecisions once entering the platform The novel contributionof our paper is to present a waiting area choice model Theforce-driven equation for passengersrsquo walking in this paper isthe SFM [23] in which both physical and motivation forcesare considered this is thus at the operational level

21 Waiting Area Choice Model for Passengers Through alarge number of investigations at the subway platform andalso analyzing the video data we discover that waiting areachoice behavior for passengers is more likely to be affectedby the passenger density in the visual field the distance tothe waiting area a cycle at the dwell time or separation timelarge pieces of luggage and other uncertain factors Eachinfluence factor can result in generating a part of cost In thispaper we assume that a passenger makes continuous choicesaccording to the real-time situations and this decision-making considers all the above influence factors

This paper first puts forward the concept of the expectedcost 119862119894119908(119905 119909 119910) for the passenger 119894 in the position (119909 119910) tochoose a waiting area 119908 at time 119905 When determining whichwaiting area the choice is governed by the expected costwhich represents a possible minimum cost is an optimalwaiting area We express 119862119894119908(119905 119909 119910) as

119862119894119908 (119905 119909 119910) = 3sum119896=1

119862119894119908119896 (119905 119909 119910) + 120585 (1)

where 119862119894119908119896 (119905 119909 119910) is the expected cost caused by detailedfactors to affect the selection of waiting areas and 120585 is anuncertain cost caused by someother uncertain factors beyondour knowledge which fits the normal function

We introduce 1198621198941199081 1198621198941199082 and 1198621198941199083 as the expected costsresulting from the distance to the waiting area the lengthof the waiting area occupied by passengers and passengerdensity in the area from hisher current position to thecorresponding waiting area shown in Figure 3 respectively

We compute 1198621198941199081 as

1198621198941199081 (119905 119909 119910) = exp(1205721 sdot 119889119894119908 (119905 119909 119910) sdot 120583 (119905 119909 119910)1205731 ) (2)

We define 119889119894119908(119905 119909 119910) as the distance from passengerrsquoscurrent position (119909 119910) to the center point of the waiting area119908 at time 119905 The influence degree of 119889119894119908(119905 119909 119910) on the waitingarea choice can also be affected by the passenger densitynearby We hypothesize that variable 120583(119905 119909 119910) represents thisinfluence it is given by (3) It can be interpreted as followswhen passengers enter the platform from the stairescalatorand then observe a large number of pedestrians gathering inthe waiting areas which are near the stairescalator they mayprefer to choose a further waiting area

120583 (119905 119909 119910) =

1 if 120588 (119905 119909 119910) le 1205880120588 (119905 119909 119910)1205880 if 120588 (119905 119909 119910) gt 1205880 (3)

4 Journal of Advanced Transportation

w-1w-2

i

w+1w w+5w+2 w+3 w+4

j

i Sw

２n２

j

Figure 3 Illustration of passenger motions at the platform

10

9

8

7

6

5

4

3

2

1

y (m

)

2 4 6 8 10

x (m)

Rn

Figure 4 Illustration of density calculation using the Voronoidiagram

Table 1 Passenger density andmobility at different levels of service

Level of service Passenger density (pm2) Passenger mobilityA le 083 Not affectedB 083-111 Slightly affectedC 111-143 Affected evadeD 143-333 Severely restrictedE 333-50 stagnationF ge 50 stagnation

where 120588(119905 119909 119910) = 119873sum119873119894=1 |119860 119894| is the passenger densitynearby within the sector area with a radius 119877119899 and isillustrated in Figure 4 Note that the density is calculated bythe Voronoi diagram [44]119873 is the number of passengers inthe sector and 119860 119894 is the area of each Voronoi cell Actuallythe radius of a vision field 119877V is usually larger than 119877119899 Wehypothesize a central angle of 2120579 = 170∘ 1205880 is determinedaccording to the level of service [45] listed in Table 1 Inthis paper we assume 1205880 = 083 pm2 When 1205880 ge 083pm2 passengers will feel uncomfortable and their mobilitieswill be restricted severely at these areas At this time someevacuation strategies will be adopted at the platform forexample public broadcasting or staff guiding passengers tosomewhere with relatively few people as shown in Figure 5

Stationworker

Ourresearcher

Waiting passengers

Searching passengers

Figure 5 Station worker guides passengers to the middle part of theplatform

1205731 is a sensitive positive parameter for scaling theexpected cost 1198621198941199081 1205721 is an inertia positive parameter whichis affected by the passengerrsquos arriving time at the platform andwhether or not they are carrying large pieces of luggageThen1205721 is expressed by

1205721=

119863119879119879119871 if (119889119908119890119897119897 (119905) = 1 or 119897119906119892119892119886119892119890 (119905) = 1) and 119889119894119908 gt 11988901 if 119900119905ℎ119890119903119904

(4)

Here 119863119879means dwell time which is defined in Figure 1and 119879119871 refers to the time left in the dwell time period119889119908119890119897119897(119905) = 1 represents a cycle at the dwell time in timeinstant 119905 otherwise at the separation time 119897119906119892119892119886119892119890(119905) = 1represents the passenger carrying large pieces of luggageotherwise not carrying When passengers at somewhere ofthe platform are informed of the coming of a train theymay prefer to choose a nearby waiting area with relativelyfew people If passengers carry large pieces of luggage whichcan result in the walking speed reducing the distance factorwill be considered as a very important influence factor inthis paper and passenger would like to choose a nearerwaiting area In this paper we hypothesize that 1198890 is a positiveconstant

The number of passengers in the waiting area is anotherimportant factor to affect the decision-making reflectedby the variable 1198621198941199082 (119905 119909 119910) We define the expression of

Journal of Advanced Transportation 5

1198621198941199082 (119905 119909 119910) as a piecewise function according to a cycle atdifferent time levels it is given by

1198621198941199082 (119905 119909 119910)

=

1205732119871119908119886119891119905119890119903 (119905) + 1205722 1119871119908 minus 119871119908

119886119891119905119890119903 (119905) if 119889119908119890119897119897 (119905) = 11205732119871119908119887119890119891119900119903119890 (119905) + 1205722 1

119871119908 minus 119871119908119887119890119891119900119903119890 (119905) if 119889119908119890119897119897 (119905) = 0

(5)

119871119908119886119891119905119890119903(119905) and 119871119908119887119890119891119900119903119890(119905) are the length of the waiting areaoccupied by passengers at the dwell time and the separationtime respectively According to our observation the lengthof queue becomes shorter with an arrival of a train 119871119908 is thephysical length of the waiting area 119908 which is determinedaccording to the structure of the platform In this paperwe only consider the situation of 119871119908 ge 119871119908119886119891119905119890119903(119905) for thesubsequent model validation and calibration 1205732 is a sensitivepositive parameter for scaling 1205722 is an inertia positiveparameter which determines the attractive ability of the leftspace of a waiting area

In this paper 119871119908119886119891119905119890119903(119905) and 119871119908119887119890119891119900119903119890(119905) are given accordingto [42]

119871119908119886119891119905119890119903 (119905) = 0694119899119908 (119905)0510 119871119908119887119890119891119900119903119890 (119905) = 0685119899119908 (119905)0546

(6)

Here 119899119908(119905) denotes at the waiting area 119908 at time 119905The passenger density 120588119894119908(119905 119909 119910) in the area 119878119908 shown

in Figure 3 is another factor that needs to be considered Let1198621198941199083 (119905 119909 119910) denote this influence factor we define this factoras

1198621198941199083 (119905 119909 119910) = exp(120588119894119908 (119905 119909 119910)1205733 ) (7)

1205733 is a sensitive positive parameter for scaling theexpected cost 1198621198941199083 Basically the alighting passengers canleave the platform within a short time and therefore theyaffect the waiting area choice behaviors mostly concentratedin the start stage of the separation time

Therefore the optimal waiting area 119908lowast for the passenger119894 is given by

119908lowast = argmin119862119894119908 119908 = 1 2 3 119899 minus 1 119899 (8)

We define 119899 as the total number of waiting areas that isrelated to the physical structure of a platform

In this paper we assume that passenger determines anoptimal waiting area from time to time until his or herdistance to the optimal waiting area is less than a detectionthreshold Behavior like changing to another waiting areaduring boarding is not considered in this paper

22 Modeling Passenger Movement In this section we willgive a brief description of the passenger driven model basedon the SFM The SFM is proposed by Helbing et al [13 23]where pedestrians are driven by three types of forces the

desired force997888rarr1198910119894 the interaction force between pedestrians

119894 and 119895 997888rarr119891 119894119895 the interaction force between the pedestrian 119894and walls 119908 997888rarr119891 119894119908 The SFM has been a prevalent microscopicsimulation model in pedestrian dynamics and is still beinginvestigated and embedded into the numerical simulationsoftware such as Anylogic [46] and FDS+Evac [29] Someself-organization phenomena are also represented throughthe application of the SFM [47] which further reveals theusability of the model

The mathematical formula of the SFM is expressed by

119898119894119889997888rarrV 119894 (119905)119889119905 = 997888rarr1198910119894 + sum

119895( =119894)

997888rarr119891 119894119895 +sum119908

997888rarr119891 119894119908 (9)

where 119898119894 is the mass of pedestrian 119894 and 997888rarrV 119894(119905) is hisher

walking velocity at time 119905 997888rarr1198910119894 indicates the pedestrianrsquoswillingness to achieve the desired speed

At the subway station we can always observe the bondedgroups such as families friends colleagues and couplesespecially on the weekends This paper also considers theeffects of bonded groups based on the SFM and we directlyadopt the bonding force proposed in [1] which has alreadybeen calibrated and validated As bonded groups could bearthe shorter distance between each other because of theirspecial relationships the bonding force 119896119887119900119899119889119894119895 has the oppositedirection of the force 119891119894119895 The force-driven equation forpassengers in the bonded group is given by

119898119894119889997888rarrV 119894 (119905)119889119905 = 997888rarr1198910119894 + sum

119895( =119894)119895isin119861(119894)

997888rarr119891 119894119895 +sum119908

997888rarr119891 119894119908+ sum119895isin119861(119894)

(119896119887119900119899119889119894119895 + 119891119887119900119899119889119894119895 ) (10)

119891119887119900119899119889119894119895 is the interaction force between passengers 119894 and 119895who belong to the set of bonded groups 119861(119894) For passengersin the same bonded group we assume that they would choosethe same waiting area

It is easy for a pedestrian to vibrate continuously ina high density crowd especially when he or she is in thebottleneck area [48] Pelechano et al introduced a ldquostoppingrulerdquo to avoid this behavior where hisher own personalitythe walking directions of others and pedestrianrsquos currentsituation were all taken into account [48] Besides a ldquorespectrdquomechanism as a self-stopping mechanism was introduced byParisi et al which reproduced the experimental data and alsoavoided the vibration [49] In this paper we adopt the sameldquorespectrdquo mechanism in [49]The respect distance119863119877 for thepassenger 119894 is 119863119877119894 = 119877119865 sdot 119903119894 where 119877119865 is the respect factorOnce any other pedestrian touches the respect area of thepedestrian 119894 which is 120587 sdot 1198632119877119894 the desired walking speed V0119894will be set to 0 until the respect area is free In this paper it isalso assumed that 119877119865 = 07 and we refer the readers to [49]for more details

When passengers arrive at the target waiting area weassume they will queue up to two columns at the mark

6 Journal of Advanced Transportation

Start

Input parameters ofthe scenario and

passengers

Calculate the simulation time

Within separation time End

Movement based on the SFM

No

Yes

Yes

Compute a target waiting area

Change the targetwaiting area

Change the desired walking

Keep the previous desiredNo

based on wlowast

walking direction rarre 0i

direction rarre 0i

Figure 6 The flow diagram of the passenger movement process at the platform

insertions of the waiting area and the desired positions willrelate to 119871119908119886119891119905119890119903(119905) or 119871119908119887119890119891119900119903119890(119905) Moreover this paper mainlyfocuses on the waiting area choice behavior of passengers atthe tactical level and the alighting and boarding behaviorsare not investigated

23 Modeling of Passenger Distribution at the Platform Pas-senger distribution at the subway platform could be predictedby the combination of waiting area choice model and passen-ger driven model The target waiting area 119908lowast determined by(8) affects a passengerrsquos desired walking direction 997888rarr119890 0119894 in theSFM In particular the flowdiagramof themovement processof passengers at the platform is shown in Figure 6 and thedetailed description is given as follows

(1) Build the platform according to the CAD diagramGenerate passengers and populate them at the plat-formnear the stairsescalatorswith randompositions

Their initial speeds are set to be 1ms and the desiredwalking directions point to the front waiting areadirectly for simplicity The number of passengersgenerated is evenly distributed over time while boththe total number of passengers and the ratio of thepassenger quantity from the left stairsescalators tothat from the right are set according to the actualdemands

(2) Calculate the simulation time If the time lengthexceeds the separation time end the simulation

(3) Compute a target waiting area 119908lowast according to thechoice model proposed in this paper Determinewhether or not changing the target waiting area Ifthe passenger keeps the previous choice of the waitingarea keep the previous desired walking directionand update the position according to the SFM Elsechange the desired walking direction according to

Journal of Advanced Transportation 7

Line 4 Line 2

Figure 7 The location of Xuanwumen subway station in the Beijing subway system

the new target waiting area Then update the newposition according to the SFM

(4) For each passenger repeat step (3) until all passengersfinish their updating

(5) Repeat steps (2) (3) and (4) until reaching therequired simulation time

3 Case Study

31 Passengersrsquo Basic Attributes According to the statisticsBeijing metro network shown in Figure 7 now has 18 lines inoperation with a total length of over 550 km In accordancewith the current plan the mileage of Beijing metro will reach997km by 2020 In addition the carrying capacity of urbanrail transit increases year by year the daily passenger volumeof Beijing subway reaches over 10000000 The platformof line 4 of Beijing Xuanwumen subway station shown inFigure 8 is chosen as an investigation platform in this paperfor the observation and data collection Xuanwumen stationis an interchange station of line 2 and line 4 Ridership atXuanwumen station is very large especially during themorn-ing and evening peak hours According to the transportationexperience in Beijing 700-900 am and 1700-1900 pm are

rush hours while the other hours are all considered as off-peak hours

In this paper we choose P0 in Figure 8 as the observationplace to collect the data of passengersrsquo basic attributes from1800 pm to 2000 pmThe collected attributes mainly consistof male-to-female ratio age structure bonding rate andluggage statistics Some statistics data are listed in Table 2This table reflects that there is not any significant difference inthe gender ratio and most passengers are young and middle-aged for about 95 because of the complex structure of thestation and the existence of stairsescalators In additionthe bonding rate is around 10 and the ratio of passengerscarrying large pieces of luggage is around 5 Passengers whotake the large pieces of luggage always have the relatively lowtravel efficiency and they mainly transfer to Beijing SouthRailway StationThemasses of passengers are set according tothe statistics data fromNational Health and Family PlanningCommission of the Peoplersquos Republic of China Moreoverother data in Table 2 are consistent with that in [50]

There are stairsescalators on both sides of the platformthrough which passengers enter or leave the platform Thefield data of the inflow and outflow from 1830 pm to 2000pm are collected at the observation places P119897 and P119903 Thesoftware SPSS is applied to test the collected data for the

8 Journal of Advanced Transportation

StairEscalator

Toilet Monitoringroom

Distributionroom

Soil body

To Tiangongyuan

To Anheqiao North

Escalator

Stair

Escalator

24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

０l

０0

０r

Figure 8 The simplified 2D diagram of the platform of line 4 at Xuanwumen subway station

Table 2 Passengersrsquo basic attributes at the platform of line 4 of Xuanwumen subway station

Passenger category Young and middle-aged (Male) Young and middle-aged (Female) Child ElderlyAge 18le age lt 60 18le age lt60 agelt18 age ge 60Proportion () 475 48 31 14Mass (kg) 66 plusmn 15 57 plusmn 15 30 plusmn 15 65 plusmn 15Radius (m) 0270 plusmn 0020 0240 plusmn 0020 0210 plusmn 0015 0250 plusmn 0020Desired speed (ms) 135 plusmn 020 115 plusmn 020 090 plusmn 030 080 plusmn 030Reaction time (s) 1 plusmn 02 1 plusmn 02 1 plusmn 02 1 plusmn 02

statistically significant correlations The testing results showthat 1198681 sim N(85 36) 1198741 sim N(78 26) 1198682 sim N(76 28) and1198742 sim N(78 27) with a 5 significance level 1198681 and 1198741respectively denote the entering and leaving numbers ofpassengers from the observation place P119897 during a cycle1198682 and 1198742 are corresponding values from P119903 in a cyclerespectivelyThemean value of 1198681 is obviously larger than thatof 1198682 which could directly result in the difference in passengerdistribution at the platform During our simulation the ratioof inflow from P119897 to that from P119903 also keeps the same valuewith our field data

32 Model Calibration This paper focuses on investigatingpassengersrsquo waiting area choice behaviors and field dataat the platform with time is collected In each cycle timethe collected data mainly contain the number of alightingpassengers 119873119908119886119897119894119892ℎ119905 the number of passengers who could notboard the train for some reason in the previous cycle time119873119908119908119886119894119905 an increase in the number of waiting passengers duringthe time between the initial of a new cycle time and beinginformed of an arrival of a train 119873119908119887119890119891119900119903119890 and an increasein the number of passengers during the time between beinginformed of the coming of a train and the open of traindoors 119873119908119894119899119888119903119890119886119904119890 Therefore the total number of passengersbefore the open of train doors in each cycle time 119873119908119903119890119886119897 is119873119908119908119886119894119905 + 119873119908119887119890119891119900119903119890 + 119873119908119894119899119888119903119890119886119904119890 Note that the station staff alwaysbroadcast the coming of a train Once broadcasting startswe will record the required 119873119908119887119890119891119900119903119890 thereby According to theobservation and statistics one reason for not boarding maybe that the space in the train is not enough for the waitingpassengers another reasonmay be that the train does not passpassengersrsquo destination station because of the operationmodeof the long-short routing In this paper we do not considerthe strategic level of their destinations but regard the resultsof these passengersrsquo choices as input data

As mentioned above large difference in the passengertraffic for two different driving directions at the platform ofline 4 of Xuanwumen subway station exists In addition thetraffic of boarding passengers with Anheqiao North directionis not very large during the evening rush hours while thetraffic of alighting passengers is relatively large We chooseto use the field data of 119873119908119887119890119891119900119903119890 119873119908119894119899119888119903119890119886119904119890 119873119908119908119886119894119905 and 119873119908119886119897119894119892ℎ119905 ineach cycle during the time from 1830 pm to 1900 pm for 24waiting areas with Anheqiao North direction at Xuanwumensubway station and the mean values of the field data andtheir corresponding approximate integer values marked byldquoestimated mean valuerdquo are shown in Figures 9 10 and 11which also indicate the position of stairs Note that there isno passenger who could not board in the dwell time For ourstatistic data in each cycle time we can find the significantdifference between the total number of waiting passengerssum24119908=1119873119908119903119890119886119897 and the alighting passengers sum24119908=1119873119908119886119897119894119892ℎ119905 Thestatistic results indicate that the mean value of sum24119908=1119873119908119887119890119891119900119903119890during a cycle time is 36 with a standard deviation 9 and themean value of sum24119908=1119873119908119894119899119888119903119890119886119904119890 is 20 with a standard deviation3 while the mean value ofsum24119908=1119873119908119886119897119894119892ℎ119905 is 153 with a standarddeviation 29 These numerical fluctuations of sum24119908=1119873119908119887119890119891119900119903119890and sum24119908=1119873119908119894119899119888119903119890119886119904119890 are not very great which provide us thepossibility of calibrating the model based on these dataThough the statistic data of the number of passengers at eachwaiting area during each cycle time always vary randomlywithin a certain range the overall distribution is similar withmore passengers on both ends of the platform

According to statistics and timetable of trains traindeparture interval is 180 s during our investigation timefrom 1830 pm to 1900 pm with Anheqiao North directionGenerally the dwell time for each train ranges from 30 s to 45s and passengers are usually informed of the coming of a trainin advance through broadcasts and displayersWe assume the

Journal of Advanced Transportation 9

The mean number of passengers before the arrival of a train

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5

Figure 9The field number of passengers at eachwaiting area beforebeing informed of the arrival of a train119873119908119887119890119891119900119903119890 with Anheqiao Northdirection

An increase in the number of passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4

Figure 10 An increase in the field number of passengers at eachwaiting area119873119908119894119899119888119903119890119886119904119890 with Anheqiao North direction

longest time for passengers knowing the coming of a trainis 55 s For the feasibility of simulations the total numberof passengers with Anheqiao North direction in a cycle timeis 56 and sum24119908=1119873119908119886119897119894119892ℎ119905 = 153 during our simulation whichkeep the same with the mean field values among which thenumber of passengers coming from the left stairescalatoris 30 and 26 passengers are from the right stairescalatorAssume that passengersrsquo waiting area choice behaviors are notaffected by passengers with the other train driving directionin this paper

Basically parameter calibration of a model is very criticalto simulations [1] Parameters in the passenger driven modelof this paper have already been adapted in [1 23] whileparameter calibration in the waiting area choice model stillrequires further investigations As shown in Section 2 1198890 12057221205731 1205732 and 1205733 are the sensitivity parameters to be calibratedThe values of these parameters are related to the probabilityof choosing a waiting area Themethod of setting parameters

The number of alighting passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 11 The field number of alighting passengers at each waitingarea119873119908119886119897119894119892ℎ119905 with Anheqiao North direction

in this paper refers to [1] experiments with different values ofabove parameters are run for the investigation of the influenceof these sensitivity parameters associatedwith the perceptionof the simulation dynamics and actual observations at theplatform Meanwhile we propose to determine the aboveparameters based on the field data and the magnitudes of1198621198941199081 1198621198941199082 and 1198621198941199083 are recorded with the repeated numericalsimulations in order to regulate the influence degree ofdifferent factors Furthermore throughminimizing themeanerror E = (sum24119908=1 |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899|)24 the parameterscould be finally determined Among which119873119908119904119894119898119906119897119886119905119894119900119899 is thesimulation result of the number of passengers at each waitingarea before the opening of train doors

During the parameter calibration the mean values of thenumbers of passengers from the left and right stairsescalatorsin the simulation runs are set according to those in Figures 910 and 11 Considering all of the above criteria parameters inthis paper are set as 1198890 = 10 1205722 = 29 1205731 = 110 1205732 = 08and 1205733 = 100

After using the above parameters the dynamic char-acteristics for passengers when searching for the waitingareas could be found in the simulation snapshots shown inFigure 12 During the first few seconds of the separationtime alighting passengers occupy the main position at theplatform as shown in Figure 12(a) After that there arepassengers entering the platform continuously and choosingan appropriate waiting area as shown in Figures 12(b) and12(c) During our field observation stairs on both sides ofthe platform mainly serve outbound passengers during theinitial stage of the separation time so does the simulation InFigure 13 the box-plot shows the field number of passengersat each waiting area before the opening of doors during eachcycle time through statistics and also the simulation resultsof a random experiment marked with magenta asterisksNote that the central red mark in Figure 13 is the medianvalue of the field number of passengers at each waiting areaand the bottom and top edges of the blue box are the 25thand 75th percentiles of all collected field data respectively

10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

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4 Journal of Advanced Transportation

w-1w-2

i

w+1w w+5w+2 w+3 w+4

j

i Sw

２n２

j

Figure 3 Illustration of passenger motions at the platform

10

9

8

7

6

5

4

3

2

1

y (m

)

2 4 6 8 10

x (m)

Rn

Figure 4 Illustration of density calculation using the Voronoidiagram

Table 1 Passenger density andmobility at different levels of service

Level of service Passenger density (pm2) Passenger mobilityA le 083 Not affectedB 083-111 Slightly affectedC 111-143 Affected evadeD 143-333 Severely restrictedE 333-50 stagnationF ge 50 stagnation

where 120588(119905 119909 119910) = 119873sum119873119894=1 |119860 119894| is the passenger densitynearby within the sector area with a radius 119877119899 and isillustrated in Figure 4 Note that the density is calculated bythe Voronoi diagram [44]119873 is the number of passengers inthe sector and 119860 119894 is the area of each Voronoi cell Actuallythe radius of a vision field 119877V is usually larger than 119877119899 Wehypothesize a central angle of 2120579 = 170∘ 1205880 is determinedaccording to the level of service [45] listed in Table 1 Inthis paper we assume 1205880 = 083 pm2 When 1205880 ge 083pm2 passengers will feel uncomfortable and their mobilitieswill be restricted severely at these areas At this time someevacuation strategies will be adopted at the platform forexample public broadcasting or staff guiding passengers tosomewhere with relatively few people as shown in Figure 5

Stationworker

Ourresearcher

Waiting passengers

Searching passengers

Figure 5 Station worker guides passengers to the middle part of theplatform

1205731 is a sensitive positive parameter for scaling theexpected cost 1198621198941199081 1205721 is an inertia positive parameter whichis affected by the passengerrsquos arriving time at the platform andwhether or not they are carrying large pieces of luggageThen1205721 is expressed by

1205721=

119863119879119879119871 if (119889119908119890119897119897 (119905) = 1 or 119897119906119892119892119886119892119890 (119905) = 1) and 119889119894119908 gt 11988901 if 119900119905ℎ119890119903119904

(4)

Here 119863119879means dwell time which is defined in Figure 1and 119879119871 refers to the time left in the dwell time period119889119908119890119897119897(119905) = 1 represents a cycle at the dwell time in timeinstant 119905 otherwise at the separation time 119897119906119892119892119886119892119890(119905) = 1represents the passenger carrying large pieces of luggageotherwise not carrying When passengers at somewhere ofthe platform are informed of the coming of a train theymay prefer to choose a nearby waiting area with relativelyfew people If passengers carry large pieces of luggage whichcan result in the walking speed reducing the distance factorwill be considered as a very important influence factor inthis paper and passenger would like to choose a nearerwaiting area In this paper we hypothesize that 1198890 is a positiveconstant

The number of passengers in the waiting area is anotherimportant factor to affect the decision-making reflectedby the variable 1198621198941199082 (119905 119909 119910) We define the expression of

Journal of Advanced Transportation 5

1198621198941199082 (119905 119909 119910) as a piecewise function according to a cycle atdifferent time levels it is given by

1198621198941199082 (119905 119909 119910)

=

1205732119871119908119886119891119905119890119903 (119905) + 1205722 1119871119908 minus 119871119908

119886119891119905119890119903 (119905) if 119889119908119890119897119897 (119905) = 11205732119871119908119887119890119891119900119903119890 (119905) + 1205722 1

119871119908 minus 119871119908119887119890119891119900119903119890 (119905) if 119889119908119890119897119897 (119905) = 0

(5)

119871119908119886119891119905119890119903(119905) and 119871119908119887119890119891119900119903119890(119905) are the length of the waiting areaoccupied by passengers at the dwell time and the separationtime respectively According to our observation the lengthof queue becomes shorter with an arrival of a train 119871119908 is thephysical length of the waiting area 119908 which is determinedaccording to the structure of the platform In this paperwe only consider the situation of 119871119908 ge 119871119908119886119891119905119890119903(119905) for thesubsequent model validation and calibration 1205732 is a sensitivepositive parameter for scaling 1205722 is an inertia positiveparameter which determines the attractive ability of the leftspace of a waiting area

In this paper 119871119908119886119891119905119890119903(119905) and 119871119908119887119890119891119900119903119890(119905) are given accordingto [42]

119871119908119886119891119905119890119903 (119905) = 0694119899119908 (119905)0510 119871119908119887119890119891119900119903119890 (119905) = 0685119899119908 (119905)0546

(6)

Here 119899119908(119905) denotes at the waiting area 119908 at time 119905The passenger density 120588119894119908(119905 119909 119910) in the area 119878119908 shown

in Figure 3 is another factor that needs to be considered Let1198621198941199083 (119905 119909 119910) denote this influence factor we define this factoras

1198621198941199083 (119905 119909 119910) = exp(120588119894119908 (119905 119909 119910)1205733 ) (7)

1205733 is a sensitive positive parameter for scaling theexpected cost 1198621198941199083 Basically the alighting passengers canleave the platform within a short time and therefore theyaffect the waiting area choice behaviors mostly concentratedin the start stage of the separation time

Therefore the optimal waiting area 119908lowast for the passenger119894 is given by

119908lowast = argmin119862119894119908 119908 = 1 2 3 119899 minus 1 119899 (8)

We define 119899 as the total number of waiting areas that isrelated to the physical structure of a platform

In this paper we assume that passenger determines anoptimal waiting area from time to time until his or herdistance to the optimal waiting area is less than a detectionthreshold Behavior like changing to another waiting areaduring boarding is not considered in this paper

22 Modeling Passenger Movement In this section we willgive a brief description of the passenger driven model basedon the SFM The SFM is proposed by Helbing et al [13 23]where pedestrians are driven by three types of forces the

desired force997888rarr1198910119894 the interaction force between pedestrians

119894 and 119895 997888rarr119891 119894119895 the interaction force between the pedestrian 119894and walls 119908 997888rarr119891 119894119908 The SFM has been a prevalent microscopicsimulation model in pedestrian dynamics and is still beinginvestigated and embedded into the numerical simulationsoftware such as Anylogic [46] and FDS+Evac [29] Someself-organization phenomena are also represented throughthe application of the SFM [47] which further reveals theusability of the model

The mathematical formula of the SFM is expressed by

119898119894119889997888rarrV 119894 (119905)119889119905 = 997888rarr1198910119894 + sum

119895( =119894)

997888rarr119891 119894119895 +sum119908

997888rarr119891 119894119908 (9)

where 119898119894 is the mass of pedestrian 119894 and 997888rarrV 119894(119905) is hisher

walking velocity at time 119905 997888rarr1198910119894 indicates the pedestrianrsquoswillingness to achieve the desired speed

At the subway station we can always observe the bondedgroups such as families friends colleagues and couplesespecially on the weekends This paper also considers theeffects of bonded groups based on the SFM and we directlyadopt the bonding force proposed in [1] which has alreadybeen calibrated and validated As bonded groups could bearthe shorter distance between each other because of theirspecial relationships the bonding force 119896119887119900119899119889119894119895 has the oppositedirection of the force 119891119894119895 The force-driven equation forpassengers in the bonded group is given by

119898119894119889997888rarrV 119894 (119905)119889119905 = 997888rarr1198910119894 + sum

119895( =119894)119895isin119861(119894)

997888rarr119891 119894119895 +sum119908

997888rarr119891 119894119908+ sum119895isin119861(119894)

(119896119887119900119899119889119894119895 + 119891119887119900119899119889119894119895 ) (10)

119891119887119900119899119889119894119895 is the interaction force between passengers 119894 and 119895who belong to the set of bonded groups 119861(119894) For passengersin the same bonded group we assume that they would choosethe same waiting area

It is easy for a pedestrian to vibrate continuously ina high density crowd especially when he or she is in thebottleneck area [48] Pelechano et al introduced a ldquostoppingrulerdquo to avoid this behavior where hisher own personalitythe walking directions of others and pedestrianrsquos currentsituation were all taken into account [48] Besides a ldquorespectrdquomechanism as a self-stopping mechanism was introduced byParisi et al which reproduced the experimental data and alsoavoided the vibration [49] In this paper we adopt the sameldquorespectrdquo mechanism in [49]The respect distance119863119877 for thepassenger 119894 is 119863119877119894 = 119877119865 sdot 119903119894 where 119877119865 is the respect factorOnce any other pedestrian touches the respect area of thepedestrian 119894 which is 120587 sdot 1198632119877119894 the desired walking speed V0119894will be set to 0 until the respect area is free In this paper it isalso assumed that 119877119865 = 07 and we refer the readers to [49]for more details

When passengers arrive at the target waiting area weassume they will queue up to two columns at the mark

6 Journal of Advanced Transportation

Start

Input parameters ofthe scenario and

passengers

Calculate the simulation time

Within separation time End

Movement based on the SFM

No

Yes

Yes

Compute a target waiting area

Change the targetwaiting area

Change the desired walking

Keep the previous desiredNo

based on wlowast

walking direction rarre 0i

direction rarre 0i

Figure 6 The flow diagram of the passenger movement process at the platform

insertions of the waiting area and the desired positions willrelate to 119871119908119886119891119905119890119903(119905) or 119871119908119887119890119891119900119903119890(119905) Moreover this paper mainlyfocuses on the waiting area choice behavior of passengers atthe tactical level and the alighting and boarding behaviorsare not investigated

23 Modeling of Passenger Distribution at the Platform Pas-senger distribution at the subway platform could be predictedby the combination of waiting area choice model and passen-ger driven model The target waiting area 119908lowast determined by(8) affects a passengerrsquos desired walking direction 997888rarr119890 0119894 in theSFM In particular the flowdiagramof themovement processof passengers at the platform is shown in Figure 6 and thedetailed description is given as follows

(1) Build the platform according to the CAD diagramGenerate passengers and populate them at the plat-formnear the stairsescalatorswith randompositions

Their initial speeds are set to be 1ms and the desiredwalking directions point to the front waiting areadirectly for simplicity The number of passengersgenerated is evenly distributed over time while boththe total number of passengers and the ratio of thepassenger quantity from the left stairsescalators tothat from the right are set according to the actualdemands

(2) Calculate the simulation time If the time lengthexceeds the separation time end the simulation

(3) Compute a target waiting area 119908lowast according to thechoice model proposed in this paper Determinewhether or not changing the target waiting area Ifthe passenger keeps the previous choice of the waitingarea keep the previous desired walking directionand update the position according to the SFM Elsechange the desired walking direction according to

Journal of Advanced Transportation 7

Line 4 Line 2

Figure 7 The location of Xuanwumen subway station in the Beijing subway system

the new target waiting area Then update the newposition according to the SFM

(4) For each passenger repeat step (3) until all passengersfinish their updating

(5) Repeat steps (2) (3) and (4) until reaching therequired simulation time

3 Case Study

31 Passengersrsquo Basic Attributes According to the statisticsBeijing metro network shown in Figure 7 now has 18 lines inoperation with a total length of over 550 km In accordancewith the current plan the mileage of Beijing metro will reach997km by 2020 In addition the carrying capacity of urbanrail transit increases year by year the daily passenger volumeof Beijing subway reaches over 10000000 The platformof line 4 of Beijing Xuanwumen subway station shown inFigure 8 is chosen as an investigation platform in this paperfor the observation and data collection Xuanwumen stationis an interchange station of line 2 and line 4 Ridership atXuanwumen station is very large especially during themorn-ing and evening peak hours According to the transportationexperience in Beijing 700-900 am and 1700-1900 pm are

rush hours while the other hours are all considered as off-peak hours

In this paper we choose P0 in Figure 8 as the observationplace to collect the data of passengersrsquo basic attributes from1800 pm to 2000 pmThe collected attributes mainly consistof male-to-female ratio age structure bonding rate andluggage statistics Some statistics data are listed in Table 2This table reflects that there is not any significant difference inthe gender ratio and most passengers are young and middle-aged for about 95 because of the complex structure of thestation and the existence of stairsescalators In additionthe bonding rate is around 10 and the ratio of passengerscarrying large pieces of luggage is around 5 Passengers whotake the large pieces of luggage always have the relatively lowtravel efficiency and they mainly transfer to Beijing SouthRailway StationThemasses of passengers are set according tothe statistics data fromNational Health and Family PlanningCommission of the Peoplersquos Republic of China Moreoverother data in Table 2 are consistent with that in [50]

There are stairsescalators on both sides of the platformthrough which passengers enter or leave the platform Thefield data of the inflow and outflow from 1830 pm to 2000pm are collected at the observation places P119897 and P119903 Thesoftware SPSS is applied to test the collected data for the

8 Journal of Advanced Transportation

StairEscalator

Toilet Monitoringroom

Distributionroom

Soil body

To Tiangongyuan

To Anheqiao North

Escalator

Stair

Escalator

24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

０l

０0

０r

Figure 8 The simplified 2D diagram of the platform of line 4 at Xuanwumen subway station

Table 2 Passengersrsquo basic attributes at the platform of line 4 of Xuanwumen subway station

Passenger category Young and middle-aged (Male) Young and middle-aged (Female) Child ElderlyAge 18le age lt 60 18le age lt60 agelt18 age ge 60Proportion () 475 48 31 14Mass (kg) 66 plusmn 15 57 plusmn 15 30 plusmn 15 65 plusmn 15Radius (m) 0270 plusmn 0020 0240 plusmn 0020 0210 plusmn 0015 0250 plusmn 0020Desired speed (ms) 135 plusmn 020 115 plusmn 020 090 plusmn 030 080 plusmn 030Reaction time (s) 1 plusmn 02 1 plusmn 02 1 plusmn 02 1 plusmn 02

statistically significant correlations The testing results showthat 1198681 sim N(85 36) 1198741 sim N(78 26) 1198682 sim N(76 28) and1198742 sim N(78 27) with a 5 significance level 1198681 and 1198741respectively denote the entering and leaving numbers ofpassengers from the observation place P119897 during a cycle1198682 and 1198742 are corresponding values from P119903 in a cyclerespectivelyThemean value of 1198681 is obviously larger than thatof 1198682 which could directly result in the difference in passengerdistribution at the platform During our simulation the ratioof inflow from P119897 to that from P119903 also keeps the same valuewith our field data

32 Model Calibration This paper focuses on investigatingpassengersrsquo waiting area choice behaviors and field dataat the platform with time is collected In each cycle timethe collected data mainly contain the number of alightingpassengers 119873119908119886119897119894119892ℎ119905 the number of passengers who could notboard the train for some reason in the previous cycle time119873119908119908119886119894119905 an increase in the number of waiting passengers duringthe time between the initial of a new cycle time and beinginformed of an arrival of a train 119873119908119887119890119891119900119903119890 and an increasein the number of passengers during the time between beinginformed of the coming of a train and the open of traindoors 119873119908119894119899119888119903119890119886119904119890 Therefore the total number of passengersbefore the open of train doors in each cycle time 119873119908119903119890119886119897 is119873119908119908119886119894119905 + 119873119908119887119890119891119900119903119890 + 119873119908119894119899119888119903119890119886119904119890 Note that the station staff alwaysbroadcast the coming of a train Once broadcasting startswe will record the required 119873119908119887119890119891119900119903119890 thereby According to theobservation and statistics one reason for not boarding maybe that the space in the train is not enough for the waitingpassengers another reasonmay be that the train does not passpassengersrsquo destination station because of the operationmodeof the long-short routing In this paper we do not considerthe strategic level of their destinations but regard the resultsof these passengersrsquo choices as input data

As mentioned above large difference in the passengertraffic for two different driving directions at the platform ofline 4 of Xuanwumen subway station exists In addition thetraffic of boarding passengers with Anheqiao North directionis not very large during the evening rush hours while thetraffic of alighting passengers is relatively large We chooseto use the field data of 119873119908119887119890119891119900119903119890 119873119908119894119899119888119903119890119886119904119890 119873119908119908119886119894119905 and 119873119908119886119897119894119892ℎ119905 ineach cycle during the time from 1830 pm to 1900 pm for 24waiting areas with Anheqiao North direction at Xuanwumensubway station and the mean values of the field data andtheir corresponding approximate integer values marked byldquoestimated mean valuerdquo are shown in Figures 9 10 and 11which also indicate the position of stairs Note that there isno passenger who could not board in the dwell time For ourstatistic data in each cycle time we can find the significantdifference between the total number of waiting passengerssum24119908=1119873119908119903119890119886119897 and the alighting passengers sum24119908=1119873119908119886119897119894119892ℎ119905 Thestatistic results indicate that the mean value of sum24119908=1119873119908119887119890119891119900119903119890during a cycle time is 36 with a standard deviation 9 and themean value of sum24119908=1119873119908119894119899119888119903119890119886119904119890 is 20 with a standard deviation3 while the mean value ofsum24119908=1119873119908119886119897119894119892ℎ119905 is 153 with a standarddeviation 29 These numerical fluctuations of sum24119908=1119873119908119887119890119891119900119903119890and sum24119908=1119873119908119894119899119888119903119890119886119904119890 are not very great which provide us thepossibility of calibrating the model based on these dataThough the statistic data of the number of passengers at eachwaiting area during each cycle time always vary randomlywithin a certain range the overall distribution is similar withmore passengers on both ends of the platform

According to statistics and timetable of trains traindeparture interval is 180 s during our investigation timefrom 1830 pm to 1900 pm with Anheqiao North directionGenerally the dwell time for each train ranges from 30 s to 45s and passengers are usually informed of the coming of a trainin advance through broadcasts and displayersWe assume the

Journal of Advanced Transportation 9

The mean number of passengers before the arrival of a train

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5

Figure 9The field number of passengers at eachwaiting area beforebeing informed of the arrival of a train119873119908119887119890119891119900119903119890 with Anheqiao Northdirection

An increase in the number of passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4

Figure 10 An increase in the field number of passengers at eachwaiting area119873119908119894119899119888119903119890119886119904119890 with Anheqiao North direction

longest time for passengers knowing the coming of a trainis 55 s For the feasibility of simulations the total numberof passengers with Anheqiao North direction in a cycle timeis 56 and sum24119908=1119873119908119886119897119894119892ℎ119905 = 153 during our simulation whichkeep the same with the mean field values among which thenumber of passengers coming from the left stairescalatoris 30 and 26 passengers are from the right stairescalatorAssume that passengersrsquo waiting area choice behaviors are notaffected by passengers with the other train driving directionin this paper

Basically parameter calibration of a model is very criticalto simulations [1] Parameters in the passenger driven modelof this paper have already been adapted in [1 23] whileparameter calibration in the waiting area choice model stillrequires further investigations As shown in Section 2 1198890 12057221205731 1205732 and 1205733 are the sensitivity parameters to be calibratedThe values of these parameters are related to the probabilityof choosing a waiting area Themethod of setting parameters

The number of alighting passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 11 The field number of alighting passengers at each waitingarea119873119908119886119897119894119892ℎ119905 with Anheqiao North direction

in this paper refers to [1] experiments with different values ofabove parameters are run for the investigation of the influenceof these sensitivity parameters associatedwith the perceptionof the simulation dynamics and actual observations at theplatform Meanwhile we propose to determine the aboveparameters based on the field data and the magnitudes of1198621198941199081 1198621198941199082 and 1198621198941199083 are recorded with the repeated numericalsimulations in order to regulate the influence degree ofdifferent factors Furthermore throughminimizing themeanerror E = (sum24119908=1 |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899|)24 the parameterscould be finally determined Among which119873119908119904119894119898119906119897119886119905119894119900119899 is thesimulation result of the number of passengers at each waitingarea before the opening of train doors

During the parameter calibration the mean values of thenumbers of passengers from the left and right stairsescalatorsin the simulation runs are set according to those in Figures 910 and 11 Considering all of the above criteria parameters inthis paper are set as 1198890 = 10 1205722 = 29 1205731 = 110 1205732 = 08and 1205733 = 100

After using the above parameters the dynamic char-acteristics for passengers when searching for the waitingareas could be found in the simulation snapshots shown inFigure 12 During the first few seconds of the separationtime alighting passengers occupy the main position at theplatform as shown in Figure 12(a) After that there arepassengers entering the platform continuously and choosingan appropriate waiting area as shown in Figures 12(b) and12(c) During our field observation stairs on both sides ofthe platform mainly serve outbound passengers during theinitial stage of the separation time so does the simulation InFigure 13 the box-plot shows the field number of passengersat each waiting area before the opening of doors during eachcycle time through statistics and also the simulation resultsof a random experiment marked with magenta asterisksNote that the central red mark in Figure 13 is the medianvalue of the field number of passengers at each waiting areaand the bottom and top edges of the blue box are the 25thand 75th percentiles of all collected field data respectively

10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

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Journal of Advanced Transportation 5

1198621198941199082 (119905 119909 119910) as a piecewise function according to a cycle atdifferent time levels it is given by

1198621198941199082 (119905 119909 119910)

=

1205732119871119908119886119891119905119890119903 (119905) + 1205722 1119871119908 minus 119871119908

119886119891119905119890119903 (119905) if 119889119908119890119897119897 (119905) = 11205732119871119908119887119890119891119900119903119890 (119905) + 1205722 1

119871119908 minus 119871119908119887119890119891119900119903119890 (119905) if 119889119908119890119897119897 (119905) = 0

(5)

119871119908119886119891119905119890119903(119905) and 119871119908119887119890119891119900119903119890(119905) are the length of the waiting areaoccupied by passengers at the dwell time and the separationtime respectively According to our observation the lengthof queue becomes shorter with an arrival of a train 119871119908 is thephysical length of the waiting area 119908 which is determinedaccording to the structure of the platform In this paperwe only consider the situation of 119871119908 ge 119871119908119886119891119905119890119903(119905) for thesubsequent model validation and calibration 1205732 is a sensitivepositive parameter for scaling 1205722 is an inertia positiveparameter which determines the attractive ability of the leftspace of a waiting area

In this paper 119871119908119886119891119905119890119903(119905) and 119871119908119887119890119891119900119903119890(119905) are given accordingto [42]

119871119908119886119891119905119890119903 (119905) = 0694119899119908 (119905)0510 119871119908119887119890119891119900119903119890 (119905) = 0685119899119908 (119905)0546

(6)

Here 119899119908(119905) denotes at the waiting area 119908 at time 119905The passenger density 120588119894119908(119905 119909 119910) in the area 119878119908 shown

in Figure 3 is another factor that needs to be considered Let1198621198941199083 (119905 119909 119910) denote this influence factor we define this factoras

1198621198941199083 (119905 119909 119910) = exp(120588119894119908 (119905 119909 119910)1205733 ) (7)

1205733 is a sensitive positive parameter for scaling theexpected cost 1198621198941199083 Basically the alighting passengers canleave the platform within a short time and therefore theyaffect the waiting area choice behaviors mostly concentratedin the start stage of the separation time

Therefore the optimal waiting area 119908lowast for the passenger119894 is given by

119908lowast = argmin119862119894119908 119908 = 1 2 3 119899 minus 1 119899 (8)

We define 119899 as the total number of waiting areas that isrelated to the physical structure of a platform

In this paper we assume that passenger determines anoptimal waiting area from time to time until his or herdistance to the optimal waiting area is less than a detectionthreshold Behavior like changing to another waiting areaduring boarding is not considered in this paper

22 Modeling Passenger Movement In this section we willgive a brief description of the passenger driven model basedon the SFM The SFM is proposed by Helbing et al [13 23]where pedestrians are driven by three types of forces the

desired force997888rarr1198910119894 the interaction force between pedestrians

119894 and 119895 997888rarr119891 119894119895 the interaction force between the pedestrian 119894and walls 119908 997888rarr119891 119894119908 The SFM has been a prevalent microscopicsimulation model in pedestrian dynamics and is still beinginvestigated and embedded into the numerical simulationsoftware such as Anylogic [46] and FDS+Evac [29] Someself-organization phenomena are also represented throughthe application of the SFM [47] which further reveals theusability of the model

The mathematical formula of the SFM is expressed by

119898119894119889997888rarrV 119894 (119905)119889119905 = 997888rarr1198910119894 + sum

119895( =119894)

997888rarr119891 119894119895 +sum119908

997888rarr119891 119894119908 (9)

where 119898119894 is the mass of pedestrian 119894 and 997888rarrV 119894(119905) is hisher

walking velocity at time 119905 997888rarr1198910119894 indicates the pedestrianrsquoswillingness to achieve the desired speed

At the subway station we can always observe the bondedgroups such as families friends colleagues and couplesespecially on the weekends This paper also considers theeffects of bonded groups based on the SFM and we directlyadopt the bonding force proposed in [1] which has alreadybeen calibrated and validated As bonded groups could bearthe shorter distance between each other because of theirspecial relationships the bonding force 119896119887119900119899119889119894119895 has the oppositedirection of the force 119891119894119895 The force-driven equation forpassengers in the bonded group is given by

119898119894119889997888rarrV 119894 (119905)119889119905 = 997888rarr1198910119894 + sum

119895( =119894)119895isin119861(119894)

997888rarr119891 119894119895 +sum119908

997888rarr119891 119894119908+ sum119895isin119861(119894)

(119896119887119900119899119889119894119895 + 119891119887119900119899119889119894119895 ) (10)

119891119887119900119899119889119894119895 is the interaction force between passengers 119894 and 119895who belong to the set of bonded groups 119861(119894) For passengersin the same bonded group we assume that they would choosethe same waiting area

It is easy for a pedestrian to vibrate continuously ina high density crowd especially when he or she is in thebottleneck area [48] Pelechano et al introduced a ldquostoppingrulerdquo to avoid this behavior where hisher own personalitythe walking directions of others and pedestrianrsquos currentsituation were all taken into account [48] Besides a ldquorespectrdquomechanism as a self-stopping mechanism was introduced byParisi et al which reproduced the experimental data and alsoavoided the vibration [49] In this paper we adopt the sameldquorespectrdquo mechanism in [49]The respect distance119863119877 for thepassenger 119894 is 119863119877119894 = 119877119865 sdot 119903119894 where 119877119865 is the respect factorOnce any other pedestrian touches the respect area of thepedestrian 119894 which is 120587 sdot 1198632119877119894 the desired walking speed V0119894will be set to 0 until the respect area is free In this paper it isalso assumed that 119877119865 = 07 and we refer the readers to [49]for more details

When passengers arrive at the target waiting area weassume they will queue up to two columns at the mark

6 Journal of Advanced Transportation

Start

Input parameters ofthe scenario and

passengers

Calculate the simulation time

Within separation time End

Movement based on the SFM

No

Yes

Yes

Compute a target waiting area

Change the targetwaiting area

Change the desired walking

Keep the previous desiredNo

based on wlowast

walking direction rarre 0i

direction rarre 0i

Figure 6 The flow diagram of the passenger movement process at the platform

insertions of the waiting area and the desired positions willrelate to 119871119908119886119891119905119890119903(119905) or 119871119908119887119890119891119900119903119890(119905) Moreover this paper mainlyfocuses on the waiting area choice behavior of passengers atthe tactical level and the alighting and boarding behaviorsare not investigated

23 Modeling of Passenger Distribution at the Platform Pas-senger distribution at the subway platform could be predictedby the combination of waiting area choice model and passen-ger driven model The target waiting area 119908lowast determined by(8) affects a passengerrsquos desired walking direction 997888rarr119890 0119894 in theSFM In particular the flowdiagramof themovement processof passengers at the platform is shown in Figure 6 and thedetailed description is given as follows

(1) Build the platform according to the CAD diagramGenerate passengers and populate them at the plat-formnear the stairsescalatorswith randompositions

Their initial speeds are set to be 1ms and the desiredwalking directions point to the front waiting areadirectly for simplicity The number of passengersgenerated is evenly distributed over time while boththe total number of passengers and the ratio of thepassenger quantity from the left stairsescalators tothat from the right are set according to the actualdemands

(2) Calculate the simulation time If the time lengthexceeds the separation time end the simulation

(3) Compute a target waiting area 119908lowast according to thechoice model proposed in this paper Determinewhether or not changing the target waiting area Ifthe passenger keeps the previous choice of the waitingarea keep the previous desired walking directionand update the position according to the SFM Elsechange the desired walking direction according to

Journal of Advanced Transportation 7

Line 4 Line 2

Figure 7 The location of Xuanwumen subway station in the Beijing subway system

the new target waiting area Then update the newposition according to the SFM

(4) For each passenger repeat step (3) until all passengersfinish their updating

(5) Repeat steps (2) (3) and (4) until reaching therequired simulation time

3 Case Study

31 Passengersrsquo Basic Attributes According to the statisticsBeijing metro network shown in Figure 7 now has 18 lines inoperation with a total length of over 550 km In accordancewith the current plan the mileage of Beijing metro will reach997km by 2020 In addition the carrying capacity of urbanrail transit increases year by year the daily passenger volumeof Beijing subway reaches over 10000000 The platformof line 4 of Beijing Xuanwumen subway station shown inFigure 8 is chosen as an investigation platform in this paperfor the observation and data collection Xuanwumen stationis an interchange station of line 2 and line 4 Ridership atXuanwumen station is very large especially during themorn-ing and evening peak hours According to the transportationexperience in Beijing 700-900 am and 1700-1900 pm are

rush hours while the other hours are all considered as off-peak hours

In this paper we choose P0 in Figure 8 as the observationplace to collect the data of passengersrsquo basic attributes from1800 pm to 2000 pmThe collected attributes mainly consistof male-to-female ratio age structure bonding rate andluggage statistics Some statistics data are listed in Table 2This table reflects that there is not any significant difference inthe gender ratio and most passengers are young and middle-aged for about 95 because of the complex structure of thestation and the existence of stairsescalators In additionthe bonding rate is around 10 and the ratio of passengerscarrying large pieces of luggage is around 5 Passengers whotake the large pieces of luggage always have the relatively lowtravel efficiency and they mainly transfer to Beijing SouthRailway StationThemasses of passengers are set according tothe statistics data fromNational Health and Family PlanningCommission of the Peoplersquos Republic of China Moreoverother data in Table 2 are consistent with that in [50]

There are stairsescalators on both sides of the platformthrough which passengers enter or leave the platform Thefield data of the inflow and outflow from 1830 pm to 2000pm are collected at the observation places P119897 and P119903 Thesoftware SPSS is applied to test the collected data for the

8 Journal of Advanced Transportation

StairEscalator

Toilet Monitoringroom

Distributionroom

Soil body

To Tiangongyuan

To Anheqiao North

Escalator

Stair

Escalator

24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

０l

０0

０r

Figure 8 The simplified 2D diagram of the platform of line 4 at Xuanwumen subway station

Table 2 Passengersrsquo basic attributes at the platform of line 4 of Xuanwumen subway station

Passenger category Young and middle-aged (Male) Young and middle-aged (Female) Child ElderlyAge 18le age lt 60 18le age lt60 agelt18 age ge 60Proportion () 475 48 31 14Mass (kg) 66 plusmn 15 57 plusmn 15 30 plusmn 15 65 plusmn 15Radius (m) 0270 plusmn 0020 0240 plusmn 0020 0210 plusmn 0015 0250 plusmn 0020Desired speed (ms) 135 plusmn 020 115 plusmn 020 090 plusmn 030 080 plusmn 030Reaction time (s) 1 plusmn 02 1 plusmn 02 1 plusmn 02 1 plusmn 02

statistically significant correlations The testing results showthat 1198681 sim N(85 36) 1198741 sim N(78 26) 1198682 sim N(76 28) and1198742 sim N(78 27) with a 5 significance level 1198681 and 1198741respectively denote the entering and leaving numbers ofpassengers from the observation place P119897 during a cycle1198682 and 1198742 are corresponding values from P119903 in a cyclerespectivelyThemean value of 1198681 is obviously larger than thatof 1198682 which could directly result in the difference in passengerdistribution at the platform During our simulation the ratioof inflow from P119897 to that from P119903 also keeps the same valuewith our field data

32 Model Calibration This paper focuses on investigatingpassengersrsquo waiting area choice behaviors and field dataat the platform with time is collected In each cycle timethe collected data mainly contain the number of alightingpassengers 119873119908119886119897119894119892ℎ119905 the number of passengers who could notboard the train for some reason in the previous cycle time119873119908119908119886119894119905 an increase in the number of waiting passengers duringthe time between the initial of a new cycle time and beinginformed of an arrival of a train 119873119908119887119890119891119900119903119890 and an increasein the number of passengers during the time between beinginformed of the coming of a train and the open of traindoors 119873119908119894119899119888119903119890119886119904119890 Therefore the total number of passengersbefore the open of train doors in each cycle time 119873119908119903119890119886119897 is119873119908119908119886119894119905 + 119873119908119887119890119891119900119903119890 + 119873119908119894119899119888119903119890119886119904119890 Note that the station staff alwaysbroadcast the coming of a train Once broadcasting startswe will record the required 119873119908119887119890119891119900119903119890 thereby According to theobservation and statistics one reason for not boarding maybe that the space in the train is not enough for the waitingpassengers another reasonmay be that the train does not passpassengersrsquo destination station because of the operationmodeof the long-short routing In this paper we do not considerthe strategic level of their destinations but regard the resultsof these passengersrsquo choices as input data

As mentioned above large difference in the passengertraffic for two different driving directions at the platform ofline 4 of Xuanwumen subway station exists In addition thetraffic of boarding passengers with Anheqiao North directionis not very large during the evening rush hours while thetraffic of alighting passengers is relatively large We chooseto use the field data of 119873119908119887119890119891119900119903119890 119873119908119894119899119888119903119890119886119904119890 119873119908119908119886119894119905 and 119873119908119886119897119894119892ℎ119905 ineach cycle during the time from 1830 pm to 1900 pm for 24waiting areas with Anheqiao North direction at Xuanwumensubway station and the mean values of the field data andtheir corresponding approximate integer values marked byldquoestimated mean valuerdquo are shown in Figures 9 10 and 11which also indicate the position of stairs Note that there isno passenger who could not board in the dwell time For ourstatistic data in each cycle time we can find the significantdifference between the total number of waiting passengerssum24119908=1119873119908119903119890119886119897 and the alighting passengers sum24119908=1119873119908119886119897119894119892ℎ119905 Thestatistic results indicate that the mean value of sum24119908=1119873119908119887119890119891119900119903119890during a cycle time is 36 with a standard deviation 9 and themean value of sum24119908=1119873119908119894119899119888119903119890119886119904119890 is 20 with a standard deviation3 while the mean value ofsum24119908=1119873119908119886119897119894119892ℎ119905 is 153 with a standarddeviation 29 These numerical fluctuations of sum24119908=1119873119908119887119890119891119900119903119890and sum24119908=1119873119908119894119899119888119903119890119886119904119890 are not very great which provide us thepossibility of calibrating the model based on these dataThough the statistic data of the number of passengers at eachwaiting area during each cycle time always vary randomlywithin a certain range the overall distribution is similar withmore passengers on both ends of the platform

According to statistics and timetable of trains traindeparture interval is 180 s during our investigation timefrom 1830 pm to 1900 pm with Anheqiao North directionGenerally the dwell time for each train ranges from 30 s to 45s and passengers are usually informed of the coming of a trainin advance through broadcasts and displayersWe assume the

Journal of Advanced Transportation 9

The mean number of passengers before the arrival of a train

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5

Figure 9The field number of passengers at eachwaiting area beforebeing informed of the arrival of a train119873119908119887119890119891119900119903119890 with Anheqiao Northdirection

An increase in the number of passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4

Figure 10 An increase in the field number of passengers at eachwaiting area119873119908119894119899119888119903119890119886119904119890 with Anheqiao North direction

longest time for passengers knowing the coming of a trainis 55 s For the feasibility of simulations the total numberof passengers with Anheqiao North direction in a cycle timeis 56 and sum24119908=1119873119908119886119897119894119892ℎ119905 = 153 during our simulation whichkeep the same with the mean field values among which thenumber of passengers coming from the left stairescalatoris 30 and 26 passengers are from the right stairescalatorAssume that passengersrsquo waiting area choice behaviors are notaffected by passengers with the other train driving directionin this paper

Basically parameter calibration of a model is very criticalto simulations [1] Parameters in the passenger driven modelof this paper have already been adapted in [1 23] whileparameter calibration in the waiting area choice model stillrequires further investigations As shown in Section 2 1198890 12057221205731 1205732 and 1205733 are the sensitivity parameters to be calibratedThe values of these parameters are related to the probabilityof choosing a waiting area Themethod of setting parameters

The number of alighting passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 11 The field number of alighting passengers at each waitingarea119873119908119886119897119894119892ℎ119905 with Anheqiao North direction

in this paper refers to [1] experiments with different values ofabove parameters are run for the investigation of the influenceof these sensitivity parameters associatedwith the perceptionof the simulation dynamics and actual observations at theplatform Meanwhile we propose to determine the aboveparameters based on the field data and the magnitudes of1198621198941199081 1198621198941199082 and 1198621198941199083 are recorded with the repeated numericalsimulations in order to regulate the influence degree ofdifferent factors Furthermore throughminimizing themeanerror E = (sum24119908=1 |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899|)24 the parameterscould be finally determined Among which119873119908119904119894119898119906119897119886119905119894119900119899 is thesimulation result of the number of passengers at each waitingarea before the opening of train doors

During the parameter calibration the mean values of thenumbers of passengers from the left and right stairsescalatorsin the simulation runs are set according to those in Figures 910 and 11 Considering all of the above criteria parameters inthis paper are set as 1198890 = 10 1205722 = 29 1205731 = 110 1205732 = 08and 1205733 = 100

After using the above parameters the dynamic char-acteristics for passengers when searching for the waitingareas could be found in the simulation snapshots shown inFigure 12 During the first few seconds of the separationtime alighting passengers occupy the main position at theplatform as shown in Figure 12(a) After that there arepassengers entering the platform continuously and choosingan appropriate waiting area as shown in Figures 12(b) and12(c) During our field observation stairs on both sides ofthe platform mainly serve outbound passengers during theinitial stage of the separation time so does the simulation InFigure 13 the box-plot shows the field number of passengersat each waiting area before the opening of doors during eachcycle time through statistics and also the simulation resultsof a random experiment marked with magenta asterisksNote that the central red mark in Figure 13 is the medianvalue of the field number of passengers at each waiting areaand the bottom and top edges of the blue box are the 25thand 75th percentiles of all collected field data respectively

10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

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6 Journal of Advanced Transportation

Start

Input parameters ofthe scenario and

passengers

Calculate the simulation time

Within separation time End

Movement based on the SFM

No

Yes

Yes

Compute a target waiting area

Change the targetwaiting area

Change the desired walking

Keep the previous desiredNo

based on wlowast

walking direction rarre 0i

direction rarre 0i

Figure 6 The flow diagram of the passenger movement process at the platform

insertions of the waiting area and the desired positions willrelate to 119871119908119886119891119905119890119903(119905) or 119871119908119887119890119891119900119903119890(119905) Moreover this paper mainlyfocuses on the waiting area choice behavior of passengers atthe tactical level and the alighting and boarding behaviorsare not investigated

23 Modeling of Passenger Distribution at the Platform Pas-senger distribution at the subway platform could be predictedby the combination of waiting area choice model and passen-ger driven model The target waiting area 119908lowast determined by(8) affects a passengerrsquos desired walking direction 997888rarr119890 0119894 in theSFM In particular the flowdiagramof themovement processof passengers at the platform is shown in Figure 6 and thedetailed description is given as follows

(1) Build the platform according to the CAD diagramGenerate passengers and populate them at the plat-formnear the stairsescalatorswith randompositions

Their initial speeds are set to be 1ms and the desiredwalking directions point to the front waiting areadirectly for simplicity The number of passengersgenerated is evenly distributed over time while boththe total number of passengers and the ratio of thepassenger quantity from the left stairsescalators tothat from the right are set according to the actualdemands

(2) Calculate the simulation time If the time lengthexceeds the separation time end the simulation

(3) Compute a target waiting area 119908lowast according to thechoice model proposed in this paper Determinewhether or not changing the target waiting area Ifthe passenger keeps the previous choice of the waitingarea keep the previous desired walking directionand update the position according to the SFM Elsechange the desired walking direction according to

Journal of Advanced Transportation 7

Line 4 Line 2

Figure 7 The location of Xuanwumen subway station in the Beijing subway system

the new target waiting area Then update the newposition according to the SFM

(4) For each passenger repeat step (3) until all passengersfinish their updating

(5) Repeat steps (2) (3) and (4) until reaching therequired simulation time

3 Case Study

31 Passengersrsquo Basic Attributes According to the statisticsBeijing metro network shown in Figure 7 now has 18 lines inoperation with a total length of over 550 km In accordancewith the current plan the mileage of Beijing metro will reach997km by 2020 In addition the carrying capacity of urbanrail transit increases year by year the daily passenger volumeof Beijing subway reaches over 10000000 The platformof line 4 of Beijing Xuanwumen subway station shown inFigure 8 is chosen as an investigation platform in this paperfor the observation and data collection Xuanwumen stationis an interchange station of line 2 and line 4 Ridership atXuanwumen station is very large especially during themorn-ing and evening peak hours According to the transportationexperience in Beijing 700-900 am and 1700-1900 pm are

rush hours while the other hours are all considered as off-peak hours

In this paper we choose P0 in Figure 8 as the observationplace to collect the data of passengersrsquo basic attributes from1800 pm to 2000 pmThe collected attributes mainly consistof male-to-female ratio age structure bonding rate andluggage statistics Some statistics data are listed in Table 2This table reflects that there is not any significant difference inthe gender ratio and most passengers are young and middle-aged for about 95 because of the complex structure of thestation and the existence of stairsescalators In additionthe bonding rate is around 10 and the ratio of passengerscarrying large pieces of luggage is around 5 Passengers whotake the large pieces of luggage always have the relatively lowtravel efficiency and they mainly transfer to Beijing SouthRailway StationThemasses of passengers are set according tothe statistics data fromNational Health and Family PlanningCommission of the Peoplersquos Republic of China Moreoverother data in Table 2 are consistent with that in [50]

There are stairsescalators on both sides of the platformthrough which passengers enter or leave the platform Thefield data of the inflow and outflow from 1830 pm to 2000pm are collected at the observation places P119897 and P119903 Thesoftware SPSS is applied to test the collected data for the

8 Journal of Advanced Transportation

StairEscalator

Toilet Monitoringroom

Distributionroom

Soil body

To Tiangongyuan

To Anheqiao North

Escalator

Stair

Escalator

24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

０l

０0

０r

Figure 8 The simplified 2D diagram of the platform of line 4 at Xuanwumen subway station

Table 2 Passengersrsquo basic attributes at the platform of line 4 of Xuanwumen subway station

Passenger category Young and middle-aged (Male) Young and middle-aged (Female) Child ElderlyAge 18le age lt 60 18le age lt60 agelt18 age ge 60Proportion () 475 48 31 14Mass (kg) 66 plusmn 15 57 plusmn 15 30 plusmn 15 65 plusmn 15Radius (m) 0270 plusmn 0020 0240 plusmn 0020 0210 plusmn 0015 0250 plusmn 0020Desired speed (ms) 135 plusmn 020 115 plusmn 020 090 plusmn 030 080 plusmn 030Reaction time (s) 1 plusmn 02 1 plusmn 02 1 plusmn 02 1 plusmn 02

statistically significant correlations The testing results showthat 1198681 sim N(85 36) 1198741 sim N(78 26) 1198682 sim N(76 28) and1198742 sim N(78 27) with a 5 significance level 1198681 and 1198741respectively denote the entering and leaving numbers ofpassengers from the observation place P119897 during a cycle1198682 and 1198742 are corresponding values from P119903 in a cyclerespectivelyThemean value of 1198681 is obviously larger than thatof 1198682 which could directly result in the difference in passengerdistribution at the platform During our simulation the ratioof inflow from P119897 to that from P119903 also keeps the same valuewith our field data

32 Model Calibration This paper focuses on investigatingpassengersrsquo waiting area choice behaviors and field dataat the platform with time is collected In each cycle timethe collected data mainly contain the number of alightingpassengers 119873119908119886119897119894119892ℎ119905 the number of passengers who could notboard the train for some reason in the previous cycle time119873119908119908119886119894119905 an increase in the number of waiting passengers duringthe time between the initial of a new cycle time and beinginformed of an arrival of a train 119873119908119887119890119891119900119903119890 and an increasein the number of passengers during the time between beinginformed of the coming of a train and the open of traindoors 119873119908119894119899119888119903119890119886119904119890 Therefore the total number of passengersbefore the open of train doors in each cycle time 119873119908119903119890119886119897 is119873119908119908119886119894119905 + 119873119908119887119890119891119900119903119890 + 119873119908119894119899119888119903119890119886119904119890 Note that the station staff alwaysbroadcast the coming of a train Once broadcasting startswe will record the required 119873119908119887119890119891119900119903119890 thereby According to theobservation and statistics one reason for not boarding maybe that the space in the train is not enough for the waitingpassengers another reasonmay be that the train does not passpassengersrsquo destination station because of the operationmodeof the long-short routing In this paper we do not considerthe strategic level of their destinations but regard the resultsof these passengersrsquo choices as input data

As mentioned above large difference in the passengertraffic for two different driving directions at the platform ofline 4 of Xuanwumen subway station exists In addition thetraffic of boarding passengers with Anheqiao North directionis not very large during the evening rush hours while thetraffic of alighting passengers is relatively large We chooseto use the field data of 119873119908119887119890119891119900119903119890 119873119908119894119899119888119903119890119886119904119890 119873119908119908119886119894119905 and 119873119908119886119897119894119892ℎ119905 ineach cycle during the time from 1830 pm to 1900 pm for 24waiting areas with Anheqiao North direction at Xuanwumensubway station and the mean values of the field data andtheir corresponding approximate integer values marked byldquoestimated mean valuerdquo are shown in Figures 9 10 and 11which also indicate the position of stairs Note that there isno passenger who could not board in the dwell time For ourstatistic data in each cycle time we can find the significantdifference between the total number of waiting passengerssum24119908=1119873119908119903119890119886119897 and the alighting passengers sum24119908=1119873119908119886119897119894119892ℎ119905 Thestatistic results indicate that the mean value of sum24119908=1119873119908119887119890119891119900119903119890during a cycle time is 36 with a standard deviation 9 and themean value of sum24119908=1119873119908119894119899119888119903119890119886119904119890 is 20 with a standard deviation3 while the mean value ofsum24119908=1119873119908119886119897119894119892ℎ119905 is 153 with a standarddeviation 29 These numerical fluctuations of sum24119908=1119873119908119887119890119891119900119903119890and sum24119908=1119873119908119894119899119888119903119890119886119904119890 are not very great which provide us thepossibility of calibrating the model based on these dataThough the statistic data of the number of passengers at eachwaiting area during each cycle time always vary randomlywithin a certain range the overall distribution is similar withmore passengers on both ends of the platform

According to statistics and timetable of trains traindeparture interval is 180 s during our investigation timefrom 1830 pm to 1900 pm with Anheqiao North directionGenerally the dwell time for each train ranges from 30 s to 45s and passengers are usually informed of the coming of a trainin advance through broadcasts and displayersWe assume the

Journal of Advanced Transportation 9

The mean number of passengers before the arrival of a train

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5

Figure 9The field number of passengers at eachwaiting area beforebeing informed of the arrival of a train119873119908119887119890119891119900119903119890 with Anheqiao Northdirection

An increase in the number of passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4

Figure 10 An increase in the field number of passengers at eachwaiting area119873119908119894119899119888119903119890119886119904119890 with Anheqiao North direction

longest time for passengers knowing the coming of a trainis 55 s For the feasibility of simulations the total numberof passengers with Anheqiao North direction in a cycle timeis 56 and sum24119908=1119873119908119886119897119894119892ℎ119905 = 153 during our simulation whichkeep the same with the mean field values among which thenumber of passengers coming from the left stairescalatoris 30 and 26 passengers are from the right stairescalatorAssume that passengersrsquo waiting area choice behaviors are notaffected by passengers with the other train driving directionin this paper

Basically parameter calibration of a model is very criticalto simulations [1] Parameters in the passenger driven modelof this paper have already been adapted in [1 23] whileparameter calibration in the waiting area choice model stillrequires further investigations As shown in Section 2 1198890 12057221205731 1205732 and 1205733 are the sensitivity parameters to be calibratedThe values of these parameters are related to the probabilityof choosing a waiting area Themethod of setting parameters

The number of alighting passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 11 The field number of alighting passengers at each waitingarea119873119908119886119897119894119892ℎ119905 with Anheqiao North direction

in this paper refers to [1] experiments with different values ofabove parameters are run for the investigation of the influenceof these sensitivity parameters associatedwith the perceptionof the simulation dynamics and actual observations at theplatform Meanwhile we propose to determine the aboveparameters based on the field data and the magnitudes of1198621198941199081 1198621198941199082 and 1198621198941199083 are recorded with the repeated numericalsimulations in order to regulate the influence degree ofdifferent factors Furthermore throughminimizing themeanerror E = (sum24119908=1 |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899|)24 the parameterscould be finally determined Among which119873119908119904119894119898119906119897119886119905119894119900119899 is thesimulation result of the number of passengers at each waitingarea before the opening of train doors

During the parameter calibration the mean values of thenumbers of passengers from the left and right stairsescalatorsin the simulation runs are set according to those in Figures 910 and 11 Considering all of the above criteria parameters inthis paper are set as 1198890 = 10 1205722 = 29 1205731 = 110 1205732 = 08and 1205733 = 100

After using the above parameters the dynamic char-acteristics for passengers when searching for the waitingareas could be found in the simulation snapshots shown inFigure 12 During the first few seconds of the separationtime alighting passengers occupy the main position at theplatform as shown in Figure 12(a) After that there arepassengers entering the platform continuously and choosingan appropriate waiting area as shown in Figures 12(b) and12(c) During our field observation stairs on both sides ofthe platform mainly serve outbound passengers during theinitial stage of the separation time so does the simulation InFigure 13 the box-plot shows the field number of passengersat each waiting area before the opening of doors during eachcycle time through statistics and also the simulation resultsof a random experiment marked with magenta asterisksNote that the central red mark in Figure 13 is the medianvalue of the field number of passengers at each waiting areaand the bottom and top edges of the blue box are the 25thand 75th percentiles of all collected field data respectively

10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

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Journal of Advanced Transportation 7

Line 4 Line 2

Figure 7 The location of Xuanwumen subway station in the Beijing subway system

the new target waiting area Then update the newposition according to the SFM

(4) For each passenger repeat step (3) until all passengersfinish their updating

(5) Repeat steps (2) (3) and (4) until reaching therequired simulation time

3 Case Study

31 Passengersrsquo Basic Attributes According to the statisticsBeijing metro network shown in Figure 7 now has 18 lines inoperation with a total length of over 550 km In accordancewith the current plan the mileage of Beijing metro will reach997km by 2020 In addition the carrying capacity of urbanrail transit increases year by year the daily passenger volumeof Beijing subway reaches over 10000000 The platformof line 4 of Beijing Xuanwumen subway station shown inFigure 8 is chosen as an investigation platform in this paperfor the observation and data collection Xuanwumen stationis an interchange station of line 2 and line 4 Ridership atXuanwumen station is very large especially during themorn-ing and evening peak hours According to the transportationexperience in Beijing 700-900 am and 1700-1900 pm are

rush hours while the other hours are all considered as off-peak hours

In this paper we choose P0 in Figure 8 as the observationplace to collect the data of passengersrsquo basic attributes from1800 pm to 2000 pmThe collected attributes mainly consistof male-to-female ratio age structure bonding rate andluggage statistics Some statistics data are listed in Table 2This table reflects that there is not any significant difference inthe gender ratio and most passengers are young and middle-aged for about 95 because of the complex structure of thestation and the existence of stairsescalators In additionthe bonding rate is around 10 and the ratio of passengerscarrying large pieces of luggage is around 5 Passengers whotake the large pieces of luggage always have the relatively lowtravel efficiency and they mainly transfer to Beijing SouthRailway StationThemasses of passengers are set according tothe statistics data fromNational Health and Family PlanningCommission of the Peoplersquos Republic of China Moreoverother data in Table 2 are consistent with that in [50]

There are stairsescalators on both sides of the platformthrough which passengers enter or leave the platform Thefield data of the inflow and outflow from 1830 pm to 2000pm are collected at the observation places P119897 and P119903 Thesoftware SPSS is applied to test the collected data for the

8 Journal of Advanced Transportation

StairEscalator

Toilet Monitoringroom

Distributionroom

Soil body

To Tiangongyuan

To Anheqiao North

Escalator

Stair

Escalator

24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

０l

０0

０r

Figure 8 The simplified 2D diagram of the platform of line 4 at Xuanwumen subway station

Table 2 Passengersrsquo basic attributes at the platform of line 4 of Xuanwumen subway station

Passenger category Young and middle-aged (Male) Young and middle-aged (Female) Child ElderlyAge 18le age lt 60 18le age lt60 agelt18 age ge 60Proportion () 475 48 31 14Mass (kg) 66 plusmn 15 57 plusmn 15 30 plusmn 15 65 plusmn 15Radius (m) 0270 plusmn 0020 0240 plusmn 0020 0210 plusmn 0015 0250 plusmn 0020Desired speed (ms) 135 plusmn 020 115 plusmn 020 090 plusmn 030 080 plusmn 030Reaction time (s) 1 plusmn 02 1 plusmn 02 1 plusmn 02 1 plusmn 02

statistically significant correlations The testing results showthat 1198681 sim N(85 36) 1198741 sim N(78 26) 1198682 sim N(76 28) and1198742 sim N(78 27) with a 5 significance level 1198681 and 1198741respectively denote the entering and leaving numbers ofpassengers from the observation place P119897 during a cycle1198682 and 1198742 are corresponding values from P119903 in a cyclerespectivelyThemean value of 1198681 is obviously larger than thatof 1198682 which could directly result in the difference in passengerdistribution at the platform During our simulation the ratioof inflow from P119897 to that from P119903 also keeps the same valuewith our field data

32 Model Calibration This paper focuses on investigatingpassengersrsquo waiting area choice behaviors and field dataat the platform with time is collected In each cycle timethe collected data mainly contain the number of alightingpassengers 119873119908119886119897119894119892ℎ119905 the number of passengers who could notboard the train for some reason in the previous cycle time119873119908119908119886119894119905 an increase in the number of waiting passengers duringthe time between the initial of a new cycle time and beinginformed of an arrival of a train 119873119908119887119890119891119900119903119890 and an increasein the number of passengers during the time between beinginformed of the coming of a train and the open of traindoors 119873119908119894119899119888119903119890119886119904119890 Therefore the total number of passengersbefore the open of train doors in each cycle time 119873119908119903119890119886119897 is119873119908119908119886119894119905 + 119873119908119887119890119891119900119903119890 + 119873119908119894119899119888119903119890119886119904119890 Note that the station staff alwaysbroadcast the coming of a train Once broadcasting startswe will record the required 119873119908119887119890119891119900119903119890 thereby According to theobservation and statistics one reason for not boarding maybe that the space in the train is not enough for the waitingpassengers another reasonmay be that the train does not passpassengersrsquo destination station because of the operationmodeof the long-short routing In this paper we do not considerthe strategic level of their destinations but regard the resultsof these passengersrsquo choices as input data

As mentioned above large difference in the passengertraffic for two different driving directions at the platform ofline 4 of Xuanwumen subway station exists In addition thetraffic of boarding passengers with Anheqiao North directionis not very large during the evening rush hours while thetraffic of alighting passengers is relatively large We chooseto use the field data of 119873119908119887119890119891119900119903119890 119873119908119894119899119888119903119890119886119904119890 119873119908119908119886119894119905 and 119873119908119886119897119894119892ℎ119905 ineach cycle during the time from 1830 pm to 1900 pm for 24waiting areas with Anheqiao North direction at Xuanwumensubway station and the mean values of the field data andtheir corresponding approximate integer values marked byldquoestimated mean valuerdquo are shown in Figures 9 10 and 11which also indicate the position of stairs Note that there isno passenger who could not board in the dwell time For ourstatistic data in each cycle time we can find the significantdifference between the total number of waiting passengerssum24119908=1119873119908119903119890119886119897 and the alighting passengers sum24119908=1119873119908119886119897119894119892ℎ119905 Thestatistic results indicate that the mean value of sum24119908=1119873119908119887119890119891119900119903119890during a cycle time is 36 with a standard deviation 9 and themean value of sum24119908=1119873119908119894119899119888119903119890119886119904119890 is 20 with a standard deviation3 while the mean value ofsum24119908=1119873119908119886119897119894119892ℎ119905 is 153 with a standarddeviation 29 These numerical fluctuations of sum24119908=1119873119908119887119890119891119900119903119890and sum24119908=1119873119908119894119899119888119903119890119886119904119890 are not very great which provide us thepossibility of calibrating the model based on these dataThough the statistic data of the number of passengers at eachwaiting area during each cycle time always vary randomlywithin a certain range the overall distribution is similar withmore passengers on both ends of the platform

According to statistics and timetable of trains traindeparture interval is 180 s during our investigation timefrom 1830 pm to 1900 pm with Anheqiao North directionGenerally the dwell time for each train ranges from 30 s to 45s and passengers are usually informed of the coming of a trainin advance through broadcasts and displayersWe assume the

Journal of Advanced Transportation 9

The mean number of passengers before the arrival of a train

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5

Figure 9The field number of passengers at eachwaiting area beforebeing informed of the arrival of a train119873119908119887119890119891119900119903119890 with Anheqiao Northdirection

An increase in the number of passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4

Figure 10 An increase in the field number of passengers at eachwaiting area119873119908119894119899119888119903119890119886119904119890 with Anheqiao North direction

longest time for passengers knowing the coming of a trainis 55 s For the feasibility of simulations the total numberof passengers with Anheqiao North direction in a cycle timeis 56 and sum24119908=1119873119908119886119897119894119892ℎ119905 = 153 during our simulation whichkeep the same with the mean field values among which thenumber of passengers coming from the left stairescalatoris 30 and 26 passengers are from the right stairescalatorAssume that passengersrsquo waiting area choice behaviors are notaffected by passengers with the other train driving directionin this paper

Basically parameter calibration of a model is very criticalto simulations [1] Parameters in the passenger driven modelof this paper have already been adapted in [1 23] whileparameter calibration in the waiting area choice model stillrequires further investigations As shown in Section 2 1198890 12057221205731 1205732 and 1205733 are the sensitivity parameters to be calibratedThe values of these parameters are related to the probabilityof choosing a waiting area Themethod of setting parameters

The number of alighting passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 11 The field number of alighting passengers at each waitingarea119873119908119886119897119894119892ℎ119905 with Anheqiao North direction

in this paper refers to [1] experiments with different values ofabove parameters are run for the investigation of the influenceof these sensitivity parameters associatedwith the perceptionof the simulation dynamics and actual observations at theplatform Meanwhile we propose to determine the aboveparameters based on the field data and the magnitudes of1198621198941199081 1198621198941199082 and 1198621198941199083 are recorded with the repeated numericalsimulations in order to regulate the influence degree ofdifferent factors Furthermore throughminimizing themeanerror E = (sum24119908=1 |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899|)24 the parameterscould be finally determined Among which119873119908119904119894119898119906119897119886119905119894119900119899 is thesimulation result of the number of passengers at each waitingarea before the opening of train doors

During the parameter calibration the mean values of thenumbers of passengers from the left and right stairsescalatorsin the simulation runs are set according to those in Figures 910 and 11 Considering all of the above criteria parameters inthis paper are set as 1198890 = 10 1205722 = 29 1205731 = 110 1205732 = 08and 1205733 = 100

After using the above parameters the dynamic char-acteristics for passengers when searching for the waitingareas could be found in the simulation snapshots shown inFigure 12 During the first few seconds of the separationtime alighting passengers occupy the main position at theplatform as shown in Figure 12(a) After that there arepassengers entering the platform continuously and choosingan appropriate waiting area as shown in Figures 12(b) and12(c) During our field observation stairs on both sides ofthe platform mainly serve outbound passengers during theinitial stage of the separation time so does the simulation InFigure 13 the box-plot shows the field number of passengersat each waiting area before the opening of doors during eachcycle time through statistics and also the simulation resultsof a random experiment marked with magenta asterisksNote that the central red mark in Figure 13 is the medianvalue of the field number of passengers at each waiting areaand the bottom and top edges of the blue box are the 25thand 75th percentiles of all collected field data respectively

10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

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Submit your manuscripts atwwwhindawicom

8 Journal of Advanced Transportation

StairEscalator

Toilet Monitoringroom

Distributionroom

Soil body

To Tiangongyuan

To Anheqiao North

Escalator

Stair

Escalator

24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

０l

０0

０r

Figure 8 The simplified 2D diagram of the platform of line 4 at Xuanwumen subway station

Table 2 Passengersrsquo basic attributes at the platform of line 4 of Xuanwumen subway station

Passenger category Young and middle-aged (Male) Young and middle-aged (Female) Child ElderlyAge 18le age lt 60 18le age lt60 agelt18 age ge 60Proportion () 475 48 31 14Mass (kg) 66 plusmn 15 57 plusmn 15 30 plusmn 15 65 plusmn 15Radius (m) 0270 plusmn 0020 0240 plusmn 0020 0210 plusmn 0015 0250 plusmn 0020Desired speed (ms) 135 plusmn 020 115 plusmn 020 090 plusmn 030 080 plusmn 030Reaction time (s) 1 plusmn 02 1 plusmn 02 1 plusmn 02 1 plusmn 02

statistically significant correlations The testing results showthat 1198681 sim N(85 36) 1198741 sim N(78 26) 1198682 sim N(76 28) and1198742 sim N(78 27) with a 5 significance level 1198681 and 1198741respectively denote the entering and leaving numbers ofpassengers from the observation place P119897 during a cycle1198682 and 1198742 are corresponding values from P119903 in a cyclerespectivelyThemean value of 1198681 is obviously larger than thatof 1198682 which could directly result in the difference in passengerdistribution at the platform During our simulation the ratioof inflow from P119897 to that from P119903 also keeps the same valuewith our field data

32 Model Calibration This paper focuses on investigatingpassengersrsquo waiting area choice behaviors and field dataat the platform with time is collected In each cycle timethe collected data mainly contain the number of alightingpassengers 119873119908119886119897119894119892ℎ119905 the number of passengers who could notboard the train for some reason in the previous cycle time119873119908119908119886119894119905 an increase in the number of waiting passengers duringthe time between the initial of a new cycle time and beinginformed of an arrival of a train 119873119908119887119890119891119900119903119890 and an increasein the number of passengers during the time between beinginformed of the coming of a train and the open of traindoors 119873119908119894119899119888119903119890119886119904119890 Therefore the total number of passengersbefore the open of train doors in each cycle time 119873119908119903119890119886119897 is119873119908119908119886119894119905 + 119873119908119887119890119891119900119903119890 + 119873119908119894119899119888119903119890119886119904119890 Note that the station staff alwaysbroadcast the coming of a train Once broadcasting startswe will record the required 119873119908119887119890119891119900119903119890 thereby According to theobservation and statistics one reason for not boarding maybe that the space in the train is not enough for the waitingpassengers another reasonmay be that the train does not passpassengersrsquo destination station because of the operationmodeof the long-short routing In this paper we do not considerthe strategic level of their destinations but regard the resultsof these passengersrsquo choices as input data

As mentioned above large difference in the passengertraffic for two different driving directions at the platform ofline 4 of Xuanwumen subway station exists In addition thetraffic of boarding passengers with Anheqiao North directionis not very large during the evening rush hours while thetraffic of alighting passengers is relatively large We chooseto use the field data of 119873119908119887119890119891119900119903119890 119873119908119894119899119888119903119890119886119904119890 119873119908119908119886119894119905 and 119873119908119886119897119894119892ℎ119905 ineach cycle during the time from 1830 pm to 1900 pm for 24waiting areas with Anheqiao North direction at Xuanwumensubway station and the mean values of the field data andtheir corresponding approximate integer values marked byldquoestimated mean valuerdquo are shown in Figures 9 10 and 11which also indicate the position of stairs Note that there isno passenger who could not board in the dwell time For ourstatistic data in each cycle time we can find the significantdifference between the total number of waiting passengerssum24119908=1119873119908119903119890119886119897 and the alighting passengers sum24119908=1119873119908119886119897119894119892ℎ119905 Thestatistic results indicate that the mean value of sum24119908=1119873119908119887119890119891119900119903119890during a cycle time is 36 with a standard deviation 9 and themean value of sum24119908=1119873119908119894119899119888119903119890119886119904119890 is 20 with a standard deviation3 while the mean value ofsum24119908=1119873119908119886119897119894119892ℎ119905 is 153 with a standarddeviation 29 These numerical fluctuations of sum24119908=1119873119908119887119890119891119900119903119890and sum24119908=1119873119908119894119899119888119903119890119886119904119890 are not very great which provide us thepossibility of calibrating the model based on these dataThough the statistic data of the number of passengers at eachwaiting area during each cycle time always vary randomlywithin a certain range the overall distribution is similar withmore passengers on both ends of the platform

According to statistics and timetable of trains traindeparture interval is 180 s during our investigation timefrom 1830 pm to 1900 pm with Anheqiao North directionGenerally the dwell time for each train ranges from 30 s to 45s and passengers are usually informed of the coming of a trainin advance through broadcasts and displayersWe assume the

Journal of Advanced Transportation 9

The mean number of passengers before the arrival of a train

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5

Figure 9The field number of passengers at eachwaiting area beforebeing informed of the arrival of a train119873119908119887119890119891119900119903119890 with Anheqiao Northdirection

An increase in the number of passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4

Figure 10 An increase in the field number of passengers at eachwaiting area119873119908119894119899119888119903119890119886119904119890 with Anheqiao North direction

longest time for passengers knowing the coming of a trainis 55 s For the feasibility of simulations the total numberof passengers with Anheqiao North direction in a cycle timeis 56 and sum24119908=1119873119908119886119897119894119892ℎ119905 = 153 during our simulation whichkeep the same with the mean field values among which thenumber of passengers coming from the left stairescalatoris 30 and 26 passengers are from the right stairescalatorAssume that passengersrsquo waiting area choice behaviors are notaffected by passengers with the other train driving directionin this paper

Basically parameter calibration of a model is very criticalto simulations [1] Parameters in the passenger driven modelof this paper have already been adapted in [1 23] whileparameter calibration in the waiting area choice model stillrequires further investigations As shown in Section 2 1198890 12057221205731 1205732 and 1205733 are the sensitivity parameters to be calibratedThe values of these parameters are related to the probabilityof choosing a waiting area Themethod of setting parameters

The number of alighting passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 11 The field number of alighting passengers at each waitingarea119873119908119886119897119894119892ℎ119905 with Anheqiao North direction

in this paper refers to [1] experiments with different values ofabove parameters are run for the investigation of the influenceof these sensitivity parameters associatedwith the perceptionof the simulation dynamics and actual observations at theplatform Meanwhile we propose to determine the aboveparameters based on the field data and the magnitudes of1198621198941199081 1198621198941199082 and 1198621198941199083 are recorded with the repeated numericalsimulations in order to regulate the influence degree ofdifferent factors Furthermore throughminimizing themeanerror E = (sum24119908=1 |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899|)24 the parameterscould be finally determined Among which119873119908119904119894119898119906119897119886119905119894119900119899 is thesimulation result of the number of passengers at each waitingarea before the opening of train doors

During the parameter calibration the mean values of thenumbers of passengers from the left and right stairsescalatorsin the simulation runs are set according to those in Figures 910 and 11 Considering all of the above criteria parameters inthis paper are set as 1198890 = 10 1205722 = 29 1205731 = 110 1205732 = 08and 1205733 = 100

After using the above parameters the dynamic char-acteristics for passengers when searching for the waitingareas could be found in the simulation snapshots shown inFigure 12 During the first few seconds of the separationtime alighting passengers occupy the main position at theplatform as shown in Figure 12(a) After that there arepassengers entering the platform continuously and choosingan appropriate waiting area as shown in Figures 12(b) and12(c) During our field observation stairs on both sides ofthe platform mainly serve outbound passengers during theinitial stage of the separation time so does the simulation InFigure 13 the box-plot shows the field number of passengersat each waiting area before the opening of doors during eachcycle time through statistics and also the simulation resultsof a random experiment marked with magenta asterisksNote that the central red mark in Figure 13 is the medianvalue of the field number of passengers at each waiting areaand the bottom and top edges of the blue box are the 25thand 75th percentiles of all collected field data respectively

10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

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Journal of Advanced Transportation 9

The mean number of passengers before the arrival of a train

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5

Figure 9The field number of passengers at eachwaiting area beforebeing informed of the arrival of a train119873119908119887119890119891119900119903119890 with Anheqiao Northdirection

An increase in the number of passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4

Figure 10 An increase in the field number of passengers at eachwaiting area119873119908119894119899119888119903119890119886119904119890 with Anheqiao North direction

longest time for passengers knowing the coming of a trainis 55 s For the feasibility of simulations the total numberof passengers with Anheqiao North direction in a cycle timeis 56 and sum24119908=1119873119908119886119897119894119892ℎ119905 = 153 during our simulation whichkeep the same with the mean field values among which thenumber of passengers coming from the left stairescalatoris 30 and 26 passengers are from the right stairescalatorAssume that passengersrsquo waiting area choice behaviors are notaffected by passengers with the other train driving directionin this paper

Basically parameter calibration of a model is very criticalto simulations [1] Parameters in the passenger driven modelof this paper have already been adapted in [1 23] whileparameter calibration in the waiting area choice model stillrequires further investigations As shown in Section 2 1198890 12057221205731 1205732 and 1205733 are the sensitivity parameters to be calibratedThe values of these parameters are related to the probabilityof choosing a waiting area Themethod of setting parameters

The number of alighting passengers

The i

dent

ifica

tion

num

ber o

f the

wai

ting

area

Mean value of field data Estimated mean value of field data

2321191715131197531

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 11 The field number of alighting passengers at each waitingarea119873119908119886119897119894119892ℎ119905 with Anheqiao North direction

in this paper refers to [1] experiments with different values ofabove parameters are run for the investigation of the influenceof these sensitivity parameters associatedwith the perceptionof the simulation dynamics and actual observations at theplatform Meanwhile we propose to determine the aboveparameters based on the field data and the magnitudes of1198621198941199081 1198621198941199082 and 1198621198941199083 are recorded with the repeated numericalsimulations in order to regulate the influence degree ofdifferent factors Furthermore throughminimizing themeanerror E = (sum24119908=1 |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899|)24 the parameterscould be finally determined Among which119873119908119904119894119898119906119897119886119905119894119900119899 is thesimulation result of the number of passengers at each waitingarea before the opening of train doors

During the parameter calibration the mean values of thenumbers of passengers from the left and right stairsescalatorsin the simulation runs are set according to those in Figures 910 and 11 Considering all of the above criteria parameters inthis paper are set as 1198890 = 10 1205722 = 29 1205731 = 110 1205732 = 08and 1205733 = 100

After using the above parameters the dynamic char-acteristics for passengers when searching for the waitingareas could be found in the simulation snapshots shown inFigure 12 During the first few seconds of the separationtime alighting passengers occupy the main position at theplatform as shown in Figure 12(a) After that there arepassengers entering the platform continuously and choosingan appropriate waiting area as shown in Figures 12(b) and12(c) During our field observation stairs on both sides ofthe platform mainly serve outbound passengers during theinitial stage of the separation time so does the simulation InFigure 13 the box-plot shows the field number of passengersat each waiting area before the opening of doors during eachcycle time through statistics and also the simulation resultsof a random experiment marked with magenta asterisksNote that the central red mark in Figure 13 is the medianvalue of the field number of passengers at each waiting areaand the bottom and top edges of the blue box are the 25thand 75th percentiles of all collected field data respectively

10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

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10 Journal of Advanced Transportation

Table 3 Scenario setting and experiment results

Scenario Passenger number(Total)

Passenger number(Left stairescalator)

Passenger number(Right stairescalator)

Proportion (In blueboxes)

Proportion (Betweenmaximum andminimum)

S1 44 23 21 97 100S2 56 30 26 823 100S3 68 36 32 763 958

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=5 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(b) t=50 s

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(c) t=100 s

Figure 12 The snapshots of the 2D passenger movement corresponding to a simulation during the model calibration t=5 s t=50 s andt=100 s Blue dot markers represent alighting passengers and red dot markers represent passengers coming from the left stairescalator whilemagenta dot markers represent passengers coming from the right stairescalator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The identification number of the waiting area

0

2

4

6

8

10

The fi

eld

num

ber o

f pas

seng

ers

Figure 13 Box-plot for the field number of passengers at eachwaiting area and the simulation results of a random experiment

Moreover the dashed lines extend to the maximum andminimum values not considering the red outliers whichare separately plotted From Figure 13 we can observe the

simulation data are all within the blue boxes which indicatesthat the waiting area choice model proposed in this papercan reflect the distribution of passengers in the waiting areasto a certain extent Considering some random factors ofpassenger movement another repeated 20 simulations arerun for each different scenario set in Table 3 In this table thetotal numbers of passengers coming from the stairsescalatorson both sides of the platform in the scenarios S1 S2 and S3are the minimum mean and maximum values of the fielddata respectively Results indicate that the majority of thesimulation data can fall in the blue boxes of the field data andoutliers only exist in very few cases Taking into account somerandom characteristics such errors are acceptable whichfurther reflect the ability and effectiveness of this model tocapture passengersrsquo characteristics of the waiting area choicebehaviors

33 Model Validation We start from the observations ofpassenger behaviors at the platform we want to achieve thesegoals by the proposed modeling method and so we take thefollowing steps in order to ensure that our simulation resultsare indeed close to observations Simulation experiments inthe case of the platform with Tiangongyuan direction whichis opposed to the mentioned Anheqiao North direction are

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Advanced Transportation 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

5

10

15

20

25

The identification number of the waiting area

The n

umbe

r of p

asse

nger

s at e

ach

wai

ting

area

Field data ＱＱＣＮ

Field data Ｑ＜ＩＬ

Field data ＱＣＨ＝ＬＭ

Simulation result ＱＭＣＧＯＦＮＣＩＨ

Figure 14The field data and simulation results at each waiting area

5 10 15 20The identification number of the waiting area

0

50

100

150

200

250

300

Tim

e (s)

0

02

04

06

08

1

Figure 15 The pseudo-color map of the variation of passengerdensity with time at each waiting area

runwith the same total number of passengers as the field datafor the model validation Also the cycle time is set accordingto the actual field data The number of passengers at eachwaiting area is recorded during the experiment Figure 14shows the collected field data in a cycle and the simula-tion results in a single experiment with the correspondingsettings and the simulation results do not have significantdifferences from the field data During the simulation thenumber of entering passengers from P119897 is set to 110 while 99passengers enter the platform from P119903 Besidessum24119908=1119873119908119908119886119894119905 =71 and the initial distribution of these passengers at theplatform during the simulation experiment keeps the samewith the field data Figure 15 shows the pseudo-color mapof the variation of the passenger density with time fromwhich we can get the information of real-time density ateach waiting area Note that during the computing of thepassenger density the area of each waiting area is different

which depends on its physical structure Figure 16 reflectspassenger dynamics at the platform in the simulation at twodifferent time instants t=20 s and t=60 s It is especiallypointed out that the black circles stand for passengers leftin the last cycle time due to the limited capacity of thecompartments or the long-short routing operation mode Itcan be found from Figure 16 that passengers coming fromthe right stairsescalators would prefer to walk to the waitingareas in the center of the platform because more passengerswere left at the right end of the platform at the beginning timeof the simulation

Another 15 simulation experiments with different settingswhich are corresponding to the field data in 15 different cycletime between 1830 pm and 2000 pm are carried out Thisfurther indicates that inflows fromP119897 and P119903 are set differentlyin each simulation experiment according to different fielddata As shown in Figure 17 the mean value E and thestandard deviation 120575 of |119873w

119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 differentwaiting areas in 15 serial simulation experiments are appliedto measure the difference among which each simulationexperiment is done repeatedly for 20 times The 119905-test is usedto guarantee that the model can predict the general passengerdistribution at the platform The result of 119905-test validates thehypothesis that E=25 as the observation value of statistics07317 is less than the test statistic value 17613 when theconfidence level is 95 In addition subfigure in Figure 17that is 120590 = (E sdot 24)sum24119908=1119873119908119903119890119886119897 is applied to measure thetotal deviation which is around 15 Furthermore another 15simulation experiments at the platform with Tiangongyuandirection using the field data in 15 different cycle timesbetween 930 am and 1100 am are carried out Note that thistime period is among the off-peak hours The correspondingcomparison results are given in Figure 18 The result of 119905-test validates the hypothesis that E=05 when the confidencelevel is 95 Besides the total deviation 120590 is about 20Inevitably the difference in the number of pedestrians at eachwaiting area between the field data and the experiment resultexists There are some reasons for this difference One reasonis the randomness characteristic of the passengersrsquo choicebehaviors Another reason is that passenger distribution atthe platform has the relationship with the entering time intothe platform During our simulation passengers enter theplatform uniformly with time which can further result in theexistence of the distribution difference Furthermore manualcollection error may also exist

Another station Shanghai natural history museum sta-tion in China is chosen to have a further test of thevalidity of the proposed model As shown in Figure 19 thisstation has 4 entrances into the platform which are a pair ofstairsescalators on both sides of the platform and anotherpair of stairs at the middle of the platform respectivelyThe field data of passenger distribution at the platform iscollected during the time period from 1400 pm to 1700pm which indicates most passengers entering the platformfrom the left stairescalator because its location is near thepark We further do simulation experiments at the platformof Shanghai natural history museum station with JinyunRoad direction and the corresponding comparison results

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

12 Journal of Advanced Transportation

123456789101112131415161718192021222324

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

(a) t=20 s1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

123456789101112131415161718192021222324(b) t=60 s

Figure 16 Illustration of 2D passenger distribution corresponding to a simulation during the model verification t=20 s and t=60 s Blackcircles stand for passengers left in the last cycle time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

1

2

3

4

5

6

7

8

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

005

01

015

02

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 17 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas

are given in Figure 20 The results of 119905-test validates thehypothesis that E=047 when the confidence level is 95which hence reflects the validity of the proposed model

The prediction result 120590 from the macroscopic level thatonly considers the distance factor in [38] is 17 which isjust the result of an experiment that is hardly representativeBesides [39] models the passenger distribution at the subwayplatform using the ant colony optimization method in whichthe mean prediction result 120590 from multiple experiments isslightly above or below 17 within the acceptable range Itis worth noting that the result 120590 obtained by the proposedmethod in this paper could also have the similar predictionaccuracy compared with that in [39] Moreover this costfunction approach could reflect more behavior dynamics ina way of considering more influence factors

4 Conclusion

In this paper we propose a cost function method to predictpassenger distribution at the subway platform which can be

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d sta

ndar

d de

viat

ions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

015

02

025

The v

alue

s of (

Elowast24

)sum

24 Ｑ=1

Ｑ ＬＦ

Figure 18 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 24 waitingareas during the off-peak time period

further for the passenger organization and the design of thelayout of the platform Through the field observation andvideo recording a survey was done at Beijing Xuanwumensubway station for the statistics of passenger attributes anddistribution at the platform Based on the collected historicaldata and video a waiting area choice model is establishedconsidering many influencing factors such as the distance tothe waiting area passenger density in the visual field andthe length of waiting area occupied by passengers Detailedindividual characteristics such as gender age and luggagethat affect the choice determination and walking dynamicsare taken into account in the waiting area choice model andthe SFM

The model calibrated and validated by the field datafrom the platform exhibits a series of stochastic and complexdynamic phenomena It captures the individual behaviorsand also clusters characteristics during the process of choos-ing a waiting area which was once very difficult to bemodeled Under 95 confidence level the absolute deviation

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Advanced Transportation 13

To Shibo Avenue

DirectionTo Jin

yun Road

Direction

PLATFORM

StairEscalator

StairEscalator

Stair Stair

3 EXIT

2 EXIT

1 EXIT

Shanghai Natural History Museum Station

PLATFORM

Figure 19 The simplified 3D diagram of Shanghai natural history museum station

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

0

02

04

06

08

1

12

14

16

The m

ean

valu

es an

d st

anda

rd d

evia

tions

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15The serial number of simulation experiment

01

02

03

The v

alue

s of (

Elowast30)

sum30 Ｑ=1

Ｑ ＬＦ

Figure 20 The values E and 120575 of |119873119908119903119890119886119897 minus 119873119908119904119894119898119906119897119886119905119894119900119899| at 30 waitingareas for Shanghai natural historymuseum station with JinyunRoaddirection

of the number of passengers at each waiting area between thefield data and the experiment data is in an acceptable rangewhich shows the validity of this model to mimic the waitingarea choice behaviors of passengers Though Beijing subwayhas currently 334 stations and on average almost 10 milliontrips per day most stations are new and many new stationshave the exactly same designs across the Peoplersquos Republic ofChina The analysis of Beijing Xuanwumen subway stationand Shanghai natural history museum station can providerelated insights into the design and the evacuation efficiencythat are relevant for the daily transportation of several hun-dred million people across China However subway systemsin US Europe and Russia look very different the methodproposed in this paper only provides a modeling idea of thepassenger distribution prediction which is also applicable toother subway stations around the world and the calibration

and validation of this model still require a research in thefuture

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by Shandong Provincial Natural Sci-ence Foundation of China under Grant ZR2018PF008 ChinaPostdoctoral Science Foundation under Grant 2018M632625and the Scientific Research Fee of Qingdao University underGrant 41117010260 The authors would also like to thankQianling Wang Min Zhou Jing Chen Hong Lu ShihangLv Chengjie Wei Zhaoquan Tang Lei Zhang Yubing WangXiaoyuWang Zhuopu Hou Xiaowei Zhang Qi Meng ShiyuNing et al in Beijing Jiaotong University as well as YanjunZhang and Huai Zhan in Beijing MTR Corporation Limitedfor the field data collection and video recording at the subwaystation

References

[1] S Xu and H B-L Duh ldquoA simulation of bonding effects andtheir impacts on pedestrian dynamicsrdquo IEEE Transactions onIntelligent Transportation Systems vol 11 no 1 pp 153ndash161 2010

[2] M Beecroft and K Pangbourne ldquoPersonal security in travelby public transport The role of traveller information andassociated technologiesrdquo IET Intelligent Transport Systems vol9 no 2 pp 167ndash174 2015

[3] S Mukherjee D Goswami and S Chatterjee ldquoA Lagrangianapproach to modeling and analysis of a crowd dynamicsrdquo IEEE

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

14 Journal of Advanced Transportation

Transactions on Systems Man and Cybernetics Systems vol 45no 6 pp 865ndash876 2015

[4] M Zhou H Dong F-Y Wang Q Wang and X YangldquoModeling and simulation of pedestrian dynamical behaviorbased on a fuzzy logic approachrdquo Information Sciences vol 360pp 112ndash130 2016

[5] N Jia L Li S Ling S Ma andW Yao ldquoInfluence of attitudinaland low-carbon factors on behavioral intention of commutingmode choice ndash A cross-city study in Chinardquo TransportationResearch Part A Policy and Practice vol 111 pp 108ndash118 2018

[6] X Yang H Dong QWang Y Chen andXHu ldquoGuided crowddynamics via modified social forcemodelrdquoPhysica A StatisticalMechanics and its Applications vol 411 no 10 pp 63ndash73 2014

[7] H Kuang M-J Cai X-L Li and T Song ldquoAsymmetric effecton single-file dense pedestrian flowrdquo International Journal ofModern Physics C vol 26 no 6 1550064 13 pages 2015

[8] Q Wang H Dong B Ning L Y Wang and G Yin ldquoTwo-Time-ScaleHybrid TrafficModels for Pedestrian Crowdsrdquo IEEETransactions on Intelligent Transportation Systems 2018

[9] P Zhang X Jian S C Wong and K Choi ldquoPotential fieldcellular automata model for pedestrian flowrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 85 no 22012

[10] D Li and B Han ldquoBehavioral effect on pedestrian evacuationsimulation using cellular automatardquo Safety Science vol 80 pp41ndash55 2015

[11] X Li F Guo H Kuang and H Zhou ldquoEffect of psychologicaltension on pedestrian counter flow via an extended costpotential field cellular automaton modelrdquo Physica A StatisticalMechanics and its Applications vol 487 pp 47ndash57 2017

[12] S Xue R Jiang B Jia Z Wang and X Zhang ldquoPedestriancounter flow in discrete space and time experiment and itsimplication for CA modellingrdquo Transportmetrica B pp 1ndash162017

[13] D Helbing and P Molnar ldquoSocial force model for pedestriandynamicsrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 51 no 5 pp 4282ndash4286 1995

[14] X Yang H Dong X Yao X Sun Q Wang and M ZhouldquoNecessity of guides in pedestrian emergency evacuationrdquoPhysica A Statistical Mechanics and its Applications vol 442pp 397ndash408 2015

[15] X Ben X Huang Z Zhuang R Yan and S Xu ldquoAgent-basedapproach for crowded pedestrian evacuation simulationrdquo IETIntelligent Transport Systems vol 7 no 1 pp 55ndash67 2013

[16] L Tan M Hu and H Lin ldquoAgent-based simulation of buildingevacuation combining human behavior with predictable spatialaccessibility in a fire emergencyrdquo Information Sciences vol 295pp 53ndash66 2015

[17] H Wang D Chen W Pan Y Xue and H He ldquoEvacuationof pedestrians from a hall by game strategy updaterdquo ChinesePhysics B vol 23 no 8 p 080505 2014

[18] D Shi W Zhang and B Wang ldquoModeling pedestrian evacua-tion by means of game theoryrdquo Journal of Statistical MechanicsTheory and Experiment vol 2017 no 4 2017

[19] J Zhou Z-K Shi and Z-S Liu ldquoA novel lattice hydrodynamicmodel for bidirectional pedestrian flow with the considerationof pedestrianrsquos memory effectrdquoNonlinear Dynamics vol 83 no4 pp 2019ndash2033 2016

[20] R Alizadeh ldquoA dynamic cellular automaton model for evacu-ation process with obstaclesrdquo Safety Science vol 49 no 2 pp315ndash323 2011

[21] X-X Jian S C Wong P Zhang K Choi H Li and X ZhangldquoPerceived cost potential field cellular automata model with anaggregated force field for pedestrian dynamicsrdquo TransportationResearch Part C Emerging Technologies vol 42 pp 200ndash2102014

[22] F Johansson A Peterson and A Tapani ldquoWaiting pedestriansin the social force modelrdquo Physica A Statistical Mechanics andits Applications vol 419 pp 95ndash107 2015

[23] D Helbing I Farkas and T Vicsek ldquoSimulating dynamicalfeatures of escape panicrdquo Nature vol 407 no 6803 pp 487ndash490 2000

[24] J Dai X Li and L Liu ldquoSimulation of pedestrian counter flowthrough bottlenecks by using an agent-based modelrdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2202ndash2211 2013

[25] M Manley Y S Kim K Christensen and A Chen ldquoAirportEmergency Evacuation Planning An Agent-Based SimulationStudy of Dirty Bomb Scenariosrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 46 no 10 pp 1390ndash14032016

[26] L Huang S C Wong M Zhang C-W Shu andW H K LamldquoRevisiting Hughesrsquo dynamic continuum model for pedestrianflow and the development of an efficient solution algorithmrdquoTransportation Research Part B Methodological vol 43 no 1pp 127ndash141 2009

[27] D-L Qiao P Zhang Z-Y Lin S C Wong and K ChoildquoA Runge-Kutta discontinuous Galerkin scheme for hyperbolicconservation laws with discontinuous fluxesrdquo Applied Mathe-matics and Computation vol 292 pp 309ndash319 2017

[28] S Gwynne E R Galea M Owen P J Lawrence and LFilippidis ldquoA review of themethodologies used in the computersimulation of evacuation from the built environmentrdquo Buildingand Environment vol 34 no 6 pp 741ndash749 1999

[29] T Korhonen S Hostikka S Heliovaara and H Ehtamo ldquoFds+evac an agent based fire evacuation modelrdquo in Pedestrian andEvacuation Dynamics 2008 pp 109ndash120 Springer 2010

[30] D Helbing L Buzna A Johansson and T Werner ldquoSelf-organized pedestrian crowd dynamics experiments simula-tions and design solutionsrdquo Transportation Science vol 39 no1 pp 1ndash24 2005

[31] J Zhang and A Seyfried ldquoComparison of intersecting pedes-trian flows based on experimentsrdquo Physica A StatisticalMechanics and its Applications vol 405 pp 316ndash325 2014

[32] C H Lui N K Fong S Lorente A Bejan and W K ChowldquoConstructal design of pedestrian evacuation from an areardquoJournal of Applied Physics vol 113 no 3 pp 384ndash393 2013

[33] K Rahman N AbdulGhani A Abdulbasah Kamil AMustafaand M A Kabir Chowdhury ldquoModelling Pedestrian TravelTime and the Design of Facilities A Queuing Approachrdquo PLoSONE vol 8 no 5 2013

[34] L-W Chen J-H Cheng and Y-C Tseng ldquoOptimal Path Plan-ning with Spatial-Temporal Mobility Modeling for Individual-Based Emergency Guidingrdquo IEEE Transactions on SystemsMan and Cybernetics Systems vol 45 no 12 pp 1491ndash15012015

[35] Q Zhang B Han and D Li ldquoModeling and simulation ofpassenger alighting and boarding movement in Beijing metrostationsrdquo Transportation Research Part C Emerging Technolo-gies vol 16 no 5 pp 635ndash649 2008

[36] S Seriani and R Fernandez ldquoPedestrian traffic managementof boarding and alighting in metro stationsrdquo TransportationResearch Part C Emerging Technologies vol 53 pp 76ndash92 2015

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Advanced Transportation 15

[37] J Wu and S Ma ldquoCrowdedness classification method forisland platform in metro stationrdquo Journal of TransportationEngineering vol 139 no 6 pp 612ndash624 2013

[38] Y Wu J Rong Z Wei and X Liu ldquoModeling passengerdistribution on subway station platform prior to the arrival oftrains inrdquo Transportation Research Board 91st Annual Meetingno 12-2000 2012

[39] X Yang H Dong and X Yao ldquoPassenger distribution mod-elling at the subway platform based on ant colony optimizationalgorithmrdquo Simulation Modelling Practice and Theory vol 77pp 228ndash244 2017

[40] T-C Chen T-S Chen and P-WWu ldquoOn data collection usingmobile robot in wireless sensor networksrdquo IEEETransactions onSystems Man and Cybernetics Systems vol 41 no 6 pp 1213ndash1224 2011

[41] D Szplett and S C Wirasinghe ldquoAn investigation of passengerinterchange and train standing time at LRT stations (i) Alight-ing boarding and platform distribution of passengersrdquo Journalof Advanced Transportation vol 18 no 1 pp 1ndash12 1984

[42] J Wu and S Ma ldquoDivision method for waiting areas onisland platforms at metro stationsrdquo Journal of TransportationEngineering vol 139 no 4 pp 339ndash349 2013

[43] S P Hoogendoorn and P H L Bovy ldquoPedestrian route-choiceand activity scheduling theory and modelsrdquo TransportationResearch Part B Methodological vol 38 no 2 pp 169ndash1902004

[44] B Steffen and A Seyfried ldquoMethods for measuring pedestriandensity flow speed and direction with minimal scatterrdquoPhysicaA Statistical Mechanics and its Applications vol 389 no 9 pp1902ndash1910 2010

[45] J J Fruin Pedestrian planning and design Metropolitan Asso-ciation of Urban Designers and Environmental Planners 1971

[46] Y Yang J Li and Q Zhao ldquoStudy on passenger flow simulationin urban subway station based on anylogicrdquo Journal of Software vol 9 no 1 pp 140ndash146 2014

[47] X Yang W Daamen S Paul Hoogendoorn H Dong andX Yao ldquoDynamic feature analysis in bidirectional pedestrianflowsrdquo Chinese Physics B vol 25 no 2 p 028901 2016

[48] N Pelechano J M Allbeck and N I Badler ldquoControllingindividual agents in high-density crowd simulationrdquo inProceed-ings of the 7th ACM SIGGRAPHEurographics Symposium onComputer Animation SCA 2007 pp 99ndash108 USA August 2007

[49] D R Parisi M Gilman and H Moldovan ldquoA modificationof the Social Force Model can reproduce experimental data ofpedestrian flows in normal conditionsrdquo Physica A StatisticalMechanics and its Applications vol 388 no 17 pp 3600ndash36082009

[50] T Korhonen and S Hostikka ldquoFire dynamcis simulator withevacuation Fds+evac technical reference andusers guiderdquo 1-1152014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom