research article development of an optimization traffic...

Research ArticleDevelopment of an Optimization Traffic Signal Cycle LengthModel for Signalized Intersections in China

Yao Wu1 Jian Lu1 Hong Chen2 and Haifei Yang1

1 Jiangsu Key Laboratory of Urban ITS Jiangsu Collaborative Innovation Center of Modern Urban Traffic TechnologiesSoutheast University Si Pai Lou No 2 Nanjing 210096 China2School of Highway Changrsquoan University Middle of Nanerhuan Road Xirsquoan 710064 China

Correspondence should be addressed to Jian Lu lujian 1972seueducn

Received 15 December 2014 Revised 4 March 2015 Accepted 13 March 2015

Academic Editor Rafael Toledo-Moreo

Copyright copy 2015 Yao Wu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The primary objective of this study is to develop an optimization traffic signal cycle lengthmodel for signalized intersections Trafficdata were collected from 50 signalized intersections in Xirsquoan city Using comprehensive delay data the optimization cycle lengthmodel is re-recalibrated to the Chinese traffic conditions based on theWebster delaymodelThe result showed that the optimizationcycle lengthmodel takes vehicle delay time pedestrian crossing time and driversrsquo anxiety into consideration To evaluate the effectsof the optimization cycle length model three intersections were selected for a simulation The delay time and queue length basedon the optimization cycle length model and the TRRL model were compared It was found that the delay times and queue lengthswith the optimization cycle length model were significantly smaller than those with the TRRL model The results suggested thatthe optimization traffic signal cycle length model was more optimal than the TRRL model

1 Background

The intersection is an important part of urban road networksthe smooth flow of which plays a key role in the vehiclespeed and operating efficiency of the entire road networkHowever during the past two decades with motorizationrapidly increasing more and more bottleneck effects havebeen exposed at intersections in urban areas In recent yearstransportation professionals in China have developed signal-ized intersections There are lots of benefits for developingthe signalized intersections On the one hand the controlafforded by the traffic lights separates the conflicting trafficflows in time and improves vehicle safety and operationefficiency on the other hand the vehicles on the approachare suspended periodically causing delays Therefore thetraffic signal cycle plays a key role in intersection trafficcontrol A reasonable cycle length can effectively alleviateor prevent traffic congestion and reduce emissions noisepollution energy consumption and travel delay time

Probabilistic cycle length calculation was first taught atthe Yale School of Highway Traffic in the 1950s and earlierwhich used the Poisson tables to determine a cycle that would

serve some percentage (based on probabilities) of waitingqueues for successive cycles [1]This is linked to the objectiveof reducing cycle failures as the authors indicate However ithas also been recommended that the method is useful only inlight traffic conditions

During the past decades several studies have been con-ducted that address traffic signal cycle length One class ofmethods seeks to minimize the delay time of vehicles atintersections [2ndash8] The most well-known and typical trafficsignal cycle lengthmodels are the TRRLmodel and theARRBmodel

The TRRLmodel [3] has been widely used In developingthe TRRLmodel for the optimalminimumdelay cycle lengthit was assumed that the effective green times of the phaseswere in the range of their respective flow ratio values TheTRRL model is given as

1198880=

15119871 + 5

1 minus 119884

(1)

where 1198880represents the optimal cycle length (sec) 119871 repre-

sents the total lost time (sec) and119884 represents the sum of thecritical flow ratio of all phases

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 954295 9 pageshttpdxdoiorg1011552015954295

2 Mathematical Problems in Engineering

TheARRBmodel [4] introduced the ldquoparking compensa-tion coefficientrdquo to the TRRLmodel and it was combinedwiththe vehicle delay time to evaluate the degree of optimizationof the signal timing program The ARRB model is given as

1198880=

(14 + 119896) + 6

1 minus 119884

(2)


sents the parking compensation coefficient and 119884 representssum of the critical flow ratio of all phases

Although the above models are widely used they havesome limitations (1) under near-saturated or saturated con-ditions the optimal cycle length formulation proposed byWebster becomes infeasible because it generates an unreason-ably large cycle length as the intersection critical flow ratioapproaches one (2) it becomes inapplicable if the intersectioncritical flow ratio is equal to or greater than one

The Highway Capacity Manual [9] also proposed thecycle length model and the delay time model of signalizedintersections The delay time model which can be applied tovariety of saturation states has been widely used The cyclelength model is based on the expected saturation thereforeit does not guarantee that the cycle length would produce theminimum delay at an intersection It is given as

119862 =

119871

1 minus [min (CSRS) RS] (3)

where 119862 represents the cycle length (sec) 119871 represents thetotal lost time (seccycle) CS represents the sumof the criticalphase traffic volumes (vehh) RS represents the referencesum flow rate (1710lowastPHFlowastfa) (vehh) PHF represents thepeak-hour factor and fa represents the area type adjustmentfactor [09 if central business district and 10 otherwise]

Day et al [8] evaluated the effectiveness and efficiency ofWebsterrsquos cycle length and the HCM intersection saturationmetric The authors showed that calculations fromWebsterrsquosmodel and the HCM provided a framework for identifyingperiods of time when the cycle length could be substantiallyshortened periods of the day when an increase in thecycle length would provide some modest improvements andperiods of the day when the cycle length was adequate andcapacity problems could be addressed by adjusting the splitsA similar study conducted by Cheng et al [7] comparedWebsterrsquos minimum delay cycle length model and the HCM2000 optimal cyclemodel and recommended an exponential-type cycle length model

Based on the idea of minimizing the delay time manyoptimization cycle length models were developed usinglinear or nonlinear regression methods and probabilisticapproaches among others [10ndash12] Lan [10] proposed anonlinear optimal cycle length Using the optimal timingvariables obtained based on the delayminimization criterionthe functional relationship between the optimal cycle lengthsand the traffic flow parameters including the intersectioncritical flow ratio the total lost time and the duration ofthe analysis period was established through a nonlinear

regression analysis The formulation was found to generatefairly accurate estimates of optimal cycle length with a57 average deviation from the analytical solutions Hanand Li [11] studied a probabilistic approach to cycle lengthoptimization Based on the idea of selecting a cycle lengththat is small enough to ensure low delay while providingadequate capacity to handle most of the fluctuating demandconditions a five-step framework was proposed for carryingout the analyses Subsequent sensitivity analyses level-of-service assessments and cycle failure rate estimations wereconducted on the basis of random demand It was found thatlonger cycle lengths did not yield the optimal delay resultsand with extremely short cycle lengths the delay was usuallyhigh because of a lack of capacity and hence frequent cyclefailures were guaranteed

A second class of methods is based on studies aimed atoptimizing the cycle length for a saturated or oversaturatedintersection [13ndash15] Chang and Lin [13] studied the optimalsignal timing for an oversaturated intersection The authorspresented a timing decision methodology which considersthe whole oversaturation period and discrete dynamic opti-mization models were developed The optimal cycle lengthand the optimal assigned green time for each approach weredetermined for the case of two-phase control It was foundthat the proposed discrete type performance index model isa more appropriate design for congested traffic signal timingcontrol

A third class of methods is based on taking the factor ofemissions fuel and other environmental factors into consid-eration when developing the cycle length model [5 6 16] Liet al [5 6] established a signal timingmodel which optimizessignal cycle length and green time by using integratedoptimization of the traffic quality fuel consumption andemission pollution It was found that when the signal cyclelength increased from 20 to 200 s there was an optimal valuecorresponding to the performance index function When thetraffic flow rate was larger the optimal signal cycle lengthcorresponding to the performance index function increasedHowever the parameters of the model are complicated anddifficult to obtain and is therefore useful for the purpose ofstudy only and is not practical in engineering practice

The fourth class of methods is based on simulation andan intelligent algorithm to optimize the cycle length or todevelop an optimization cycle length model [17ndash19] Usingthe theory analysis and computer simulation test Yang et al[19] established a delaying calculation model of through run-ning and left-turning vehicles on a roundabout Based on themodel an optimal cycle length calculation method targetingminimum delay was derived which was suitable for the mul-tiapproach going in coordination with roundabout controlsPark et al [17] evaluated a stochastic signal optimizationmethod based on a genetic algorithm using the microscopicsimulation program CORSIM According to the method thecycle length the green ratio and the phase difference wereoptimized at the same time Kim et al [18] compared theperformance between an artificial neural network (ANN) andanalytical models for real-time cycle length design It wasfound that the ANN model provides optimal cycle lengthsstably adjusted by the minimum value the maximum value

Mathematical Problems in Engineering 3

and the cycle increment while the analytical model promotescongestion under certain operational conditions

As can be seen by the brief general discussion abovemost of the previous studies focused on the optimal cyclelength A variety of methods and models were put forwardeither based on the minimum delay time or minimum emis-sion or considering the oversaturation consideration of anintersection Even though previous studies have to someextent improved the traffic signal cycle they suffer fromseveral limitations The literature review indicated that thefollowing issues have not been addressed in previous studies(1)most of the previous cycle lengthmodels only aimed at onetarget (minimum delay time or minimum emission) or onlyapplied to the saturation status however a cycle lengthmodelof a different status was not considered and (2) most of thecycle length models did not consider the factor of pedestriancrossing and that a long cycle length would cause driver anx-iety which could reduce the traffic safety of the intersection

The primary objective of this study was to develop andevaluate a new optimization traffic signal cycle length forsignalized intersections in China More specifically the studypresented in this paper focused on the following two tasks(1) to develop an optimization traffic cycle length model forsignalized intersections and (2) to evaluate the effects of theoptimization cycle length model

2 Data Collection

Field data collection was conducted at 50 signalized inter-sections in Xirsquoan which is one of the typical biggest cities inChina The sites were carefully selected such that their geo-metric design and traffic control feathers represent the mostcommon situations in major cities in China To achieve theresearch objective the following criteria were applied in thesite selection process

(1) The selected intersection should be a typical sig-nalized intersection (ie four-leg intersection or T-leg intersection) Roundabouts and other deformityintersections must not be included

(2) The selected signalized intersections should includedifferent types (ie where different grade roads inter-sect) for example the intersection of amain road anda minor arterial road and the intersection of a mainroad and branch road

(3) Two hours of traffic data of each selected sites shouldbe recorded in peak period

The traffic data of the selected signalized intersectionincluding the traffic volume delay time cycle length greensplit and saturation were investigated among which thedirect traffic data were traffic volume and cycle length and theindirect traffic data were delay time green split and satura-tionThe calculation methods of the indirect traffic data wereshown as follows

Delay Time The individual sample survey method was usedto determine the delay time which is given as

119863 = 119873 lowast 119905

119889 =

119863

119881

(4)

where119863 represents the total delay time and119873 represents thetotal number of suspended vehicles 119905 represents the intervaltime 119889 the average delay time of each vehicle at the approachand 119881 represents the total volume at the approach

Green Split The green split is given as

120582 =

119892

119862

(5)

where 120582 represents the green split 119892 represents the effectivegreen time and 119862 represents the cycle length

Saturation The saturation is given as

119909119894=

119902119894

120582119894119904119894

(6)

119883 = max 119909119894 119894 = 1 2 3 119899 (7)

where 119909119894represents the saturation for phase 119894 119902

119894represents

the traffic volume 120582119894represents the green split 119904

119894represents

the saturation traffic volume and119883 represents the saturationdegree of the intersection

In order to collect all the traffic data mentioned abovethe following detailed information were collected during theinvestigation (1) the exact time at which each phase beganand ended as well as the cycle time (2) the number ofvehicles at every approach of each intersection at 15-minuteintervals and (3) the number of delayed vehicles at everyapproach at 15-second intervals as well as the number ofqueued vehicles and nonqueued vehicles The data collectionresults are shown in Table 1

3 Optimization Traffic Signal CycleLength Model

In the Webster delay model the average delay time consistsof three components the delay time due to the uniformtraffic flow (119889

1) the delay time due to the random traffic

flow (1198892) and compensation term due to the different traffic

environment (1198893) Thus the Webster delay model should be

corrected according to the traffic conditions in China Threeparameters 120572 120573 and 120574 were introduced 120572 is the correctioncoefficient of the first component of delay time 120573 is thecorrection coefficient of the second component of delay time


Table 1 Data collection results

Sites number Traffic parameters119902 119889 120582 119862 119883

1 2400 2646 050 120 0642 1470 5392 028 160 0703 990 5607 020 120 0814 1835 3677 036 120 0855 1150 3784 032 110 0476 1207 3389 045 160 0607 1600 2298 068 180 0928 1490 2406 065 120 0929 870 1105 055 80 02110 630 2557 036 100 02311 2065 1776 072 155 09012 185 1049 047 60 01813 790 1805 050 75 08214 845 1494 047 60 08115 1845 3708 051 100 09816 1530 3374 050 105 09817 770 2022 056 95 08518 1540 3725 056 95 07019 410 1249 041 60 03520 770 1415 042 60 06721 875 1943 041 75 07322 745 2403 042 100 06523 745 3692 041 130 06324 1180 3373 033 110 07625 1040 4136 031 120 06426 1395 4036 039 120 09627 495 2405 031 90 03028 735 4418 033 150 04729 1025 3762 016 80 03230 1805 3675 031 120 05131 2503 2201 055 120 06932 1439 6619 027 170 06733 1054 6008 019 130 08834 1770 3817 033 120 07735 1184 1207 061 110 04536 1063 3416 044 140 05637 2810 6132 036 170 08338 1865 3728 054 130 09539 891 1276 056 80 01940 683 2663 033 95 02441 2236 2527 068 170 08842 198 1190 046 60 01743 720 1864 051 70 08644 888 1911 042 75 07945 1716 3955 053 100 09646 1971 3640 046 120 09847 1710 5843 056 90 09148 1462 1964 054 100 07549 441 1625 043 60 03250 755 1754 040 60 063119902 represents the maximum traffic volume of the intersection in 15minutespcu15min119889 represents the average delay time of each vehicle s120582 represents the maximum green split119862 represents the cycle length of the saturation s119883 represents the saturation degree of the intersection

120574 is the correction coefficient of the third component of delaytime The corrected Webster delay model is given as

119889 = 1205721198891+ 1205731198892+ 1205741198893

1198891=

119862 (1 minus 120582)2

2 (1 minus 120582119909)

1198892=

1199092

2119902 (1 minus 119909)

1198893= minus065 (

119862

1199022)

13

1199092+5120582

(8)

where 119889 represents the average vehicle delay time 1198891repre-

sents the uniform delay time 1198892represents the random delay

time 1198893represents the delay compensation value 120572 120573 and 120574

represent the unknown coefficient and the other parametersare as above

As can be seen the model is a multivariate linear regres-sion equation Thus the unknown coefficient can be cali-brated using the least square method The Matlab softwarepackage was used for the data mining processThe result is asfollows

119889119894= 116

119862 (1 minus 120582119894)2

2 (1 minus 120582119894119909119894)

+ 066

1199092

119894

2119902119894(1 minus 119909

119894)

minus 079(

119862

1199022

119894

)

13

1199092+5120582119894

119894

(9)

The green time split 120582119894is given as

120582119894=

119892119894

119862

=

119862 minus 119871

119862

119910119894

119884

= (1 minus

119871

119862

)

119910119894

119884

(10)

where 119871 represents the total lost time 119892119894represents the green

time for phase 119894 119910119894represents the maximum traffic volume

ratio for phase 119894 which can be calculated by 119910119894= 119902119894119904119894 and 119884

represents the sum of traffic volume ratio of all phasesThus the saturation in (6) can be calculated as

119909119894=

119902119894

120582119894119904119894

=

119902119894

119904119894(1 minus 119871119862) (119910

119894119884)

=

119910119894

(1 minus 119871119862) (119910119894119884)

=

119884

(1 minus 119871119862)

(11)

Therefore (9) can be rewritten as

119889119894= 116

119862 (1 minus 120582119894)2

2 (1 minus 119910119894)

+ 066

(119884 (1 minus 119871119862))2

2119902119894(1 minus 119884 (1 minus 119871119862))

minus 079(

119862

1199022

119894

)

13

(

119884

1 minus 119871119862

)

2+5120582119894

(12)

The assumption for the optimization cycle length modelis that the total delay of all the phases should be minimizedwhich is given as

Min 119889total = Minsum119894

119902119894119889119894 (13)


Phase one

Phase two

Phase one Phase one

Phase two

Phase two

Phase threePhase three

Cuih

ua R

d

Xiaozhai Rd

Phase four

FengchengFive Rd

Nor

thTa

ihua

Rd

Science andTechnology

Rd

Sout

h Ta

ibai

Rd

(I) (II) (III)

Figure 1 Geometric characteristics and signal phase of the selected sites

where 119889total represents the total delay time of all phases 119902119894

represents the traffic volume and 119889119894represents the delay time

of phase 119894As can be seen from (12) the total delay 119889total is a function

of only one parameter 119862 Therefore the optimum of (13) canbe found at 120597119889total120597119862 = 0

Thus the parameter 119862 is given as

119862 =

145119871 + 3

1 minus 119884

(14)

where 119871 represents the total lost time and 119884 represents thesum of traffic volume ratio of all phases

According to (9) when the saturation 119909119894is close to 1 the

delay will tend to be infinity It is implausible and not realisticThence (14) does not apply to all the traffic conditions Thecycle length model should be rewritten as follows

119862 =

145119871 + 3

1 minus 119884

subject to 119862min le 119862 le 119862max (15)

The 119862min and 119862max are disused as follows(1) When the traffic volume is low the important consid-

eration is the pedestrian rather than the vehicle Thereforethe crossing time for the pedestrian should be focused onTheminimumgreen time for the pedestrian crossing on the streetis given as

119892min = 7 +119871119901

V119901

(16)

Therefore the cycle length can be calculated as

119862min = sum119894

(7 +

119871119901

V119901

) + 119871 (17)

where 119871119901represents length of the crossing street for the

pedestrians V119901represents the average speed of the pedestrian

and 119871 represents the total lost time(2) When the saturation is large which represents a

crowded traffic flow environment it is no longer able to solvethe problem of traffic congestion by optimal cycle length Ifthe signal control remains the main factor for determining

the cycle length should focus on avoiding the anxiety of driv-ers for waiting a long timeTherefore the suggested optimiza-tion cycle length is 180 seconds [4 20] that is 119862max = 180

In summary the optimization traffic signal cycle lengthmodel is given as

119862 =

145119871 + 3

1 minus 119884


with

119862min = sum119894

(7 +

119871119901

V119901

) + 119871

119862max = 180

(19)

Note that the development process of optimization trafficsignal cycle length model is not dependent on any particularphase-control scheme Therefore it is for 2-phase- 3-phase-and 4-phase-control signalized intersection

The green time for the above three cases is determined asfollows

The total green time is 119892total = 119862 minus 119871 thus the green timefor phase 119894 is given as

119892119894= 119892min119894 = 7 +

119871119901119894

V119901119894

for 119888 = 119862min

119892119894= (119862 minus 119871)

119910119894

119884

for 119888 = 119862 119888 = 119862min subject to 119892119894 ge 119892min119894

(20)

4 Evaluation of the Optimization TrafficSignal Cycle Length Model

41 Simulation Experimental Design In order to evaluate theeffect of the optimization traffic signal cycle length model(termed ldquoNEW modelrdquo) the traffic microsimulation tech-nology was used The experiment was conducted using thesimulation software package VISSIMThree signalized inter-sections were selected for the simulation models Geometriccharacteristics and phase-control scheme of the three selectedsites are shown in Figure 1 Traffic volume and the cycle length


Table 2 Information for the selected signalized intersections

Intersection Approaches Traffic volume (pcuh) Cycle length (sec)LT TM RT TRRL model NEWmodel

Fengcheng Five Rd and NorthTaihua Rd (I)

Westbound 72 341 124

30 40Northbound 73 545 151Eastbound 61 350 117Southbound 55 474 157

Xiaozhai Rd and Cuihua Rd (II)



Science and Technology Rd andSouth Taibai Rd (III)



are given in Table 2 Note that the cycle length was calculatedusing the NEW model As a comparison the cycle lengthcalculated using the TRRL model which is the traditionaltraffic signal cycle length model was also given in Table 2

The intersection of Fengcheng Five Rd and North TaihuaRd (termed ldquoIrdquo) is a no-busy intersection with a low trafficvolume The intersection of Science and Technology Rd andSouth Taibai Rd (termed ldquoIIIrdquo) is a very busy intersectionwith a high traffic volume The intersection of XiaozhaiRd and Cuihua Rd (termed ldquoIIrdquo) is a medium traffic flowintersection The three signalized intersections which werecarefully selected can meet the different case of the opti-mization traffic signal cycle length model The phase-controlschemes for the three intersections are 2-phase-control 3-phase-control and 4-phase-control schemes respectivelyTherefore the selected intersection can also verify the adap-tion of the optimization cycle length model for all phase-control schemes

There were two signal programs (termed ldquoTRRL modelprogramrdquo and ldquoNEWmodel programrdquo) for each intersectionThe traffic volume phase design and other signal timingalgorithm were the same The only difference was the cyclelength for which one program used the TRRL model whilethe other program using the NEW model For both signalprograms five one-hour simulation runs were completedwith unique random seeds Of the five simulation runs theones with the highest and the lowest resulting delay times arediscarded and the remaining three were averaged to obtainthe final results

42 Statistical Methods 119905-tests were conducted to identifywhether the difference in delay time and the queue lengthat signalized intersections with the TRRL model and theNEWcycle lengthmodel was statistically significantThe nullhypothesis of the tests was that the average delay time (queuelength) based on the two programs is the same The nullhypothesis can be rejected if [21]

119905 =

100381610038161003816100381610038161198831minus 1198832

10038161003816100381610038161003816

radic1199042

11198991+ 1199042

21198992

ge 1199051205722 (21)

where 120572 is the level of significance1198831and119883

2are the average

delay time (queue length) with the TRRL model and theNEW model respectively 119904

1and 1199042are the sample standard

deviations 1198991and 1198992are the number of simulation data with

TRRLmodel and theNEWmodel respectively and 1199051205722

is the100(1 minus 1205722) percentile of the 119905 distribution with degrees offreedom given by

df =(1199042

11198991+ 1199042

21198992)

2

(1199042

11198991)2 (1198991minus 1) + (119904

2

21198992)2 (1198992minus 1)

(22)

5 Data Analysis Results

Through the microsimulation using VISSIM software pack-age the research team obtained 900 data records for delaytime and 900 data records for queue length both of whichwere used for future data study Cross-sectional analysis wasconducted to compare the delay time and queue length of thetwo programs

51 Result of Delay Time The summary statistics of the delaytime for each selected intersection based on the two programswas shown in Table 3The average delay timea for the selectedintersections based on the TRRL model program were 3643451 and 5013 respectively Correspondingly the averagedelay times for the selected intersections based on the NEWmodel program were 427 3108 and 4258 respectively Thedata in Table 3 suggested that the average delay times of IIintersection and III intersection based on the NEW modelprogram were smaller than those based on the TRRL modelprogram However the average delay time of I intersectionbased on theNEWmodel programwas larger than that basedon the TRRL mode program

A series of 119905-tests were conducted to identify whether thedifferences in the delay times between the different programswere statistically significant The results of the 119905-tests wereshown in Table 4 With a 95 level of confidence the 119905-testsresults showed that the difference between delay times ofthe two programs for II intersection and III intersection wasfound to be statistically significant However the difference


Table 3 Summary statistics of delay time (secper vehicle)

Model Statistical index Intersection Sample size Maximum Minimum Mean Standard

TRRL model Delay timeI 120 1330 020 364 247II 150 648 54 3451 1304III 180 1449 206 5013 2584

NEWmodel Delay timeI 120 116 02 427 261II 150 794 95 3108 1257III 180 1352 194 4258 2063

Table 4 Results of 119905-tests for delay time

Intersection Statistical indexMean value

P valueTRRLmodel

NEWmodel

I Delay time 364 427 0054II Delay time 3451 3108 0021III Delay time 5013 4258 0002

between delay times of the two programs for I intersectionwas found to be not statistically significant The resultsindicate that the NEW model significantly affected the delaytime and was more optimal than that of the TRRL model

52 Result of Queue Length The summary statistics of thequeue length for each selected intersection based on the twoprograms was shown in Table 5 The average queue lengthsfor the selected intersections based on the TRRL modelprogram were 274 812 and 1598 respectively Correspond-ingly the average queue lengths for the selected intersectionsbased on the NEW model program were 324 604 and1002 respectively According to the data in Table 5 the queuelengths of II intersection and III intersection based on theNEW model program were smaller than those based onthe TRRL model program However the queue length of Iintersection based on the NEW model program was largerthan that based on the TRRL model program

To identify whether the differences in queue lengthsbetween different programs were statistically significant 119905-tests were then conducted The results of 119905-tests were shownin Table 6 With a 95 level of confidence the 119905-tests resultsshowed that the difference between queue lengths of thetwo programs for II intersection and III intersection wasfound to be statistically significant However the differencebetween queue lengths of the two programs for I intersectionwas found to be not statistically significant The resultswere similar to the results of delay time The result furtherdemonstrated that the NEWmodel is more optimal than theTRRL model

6 Summary and Conclusions

The study presented in this paper proposed an optimizationtraffic signal cycle length model for signalized intersection

The effect of the new model was studied through the use oftraffic microsimulation technology Cross-sectional analysiswas conducted to compare the impacts of both the traditionaltraffic signal cycle length and the optimization traffic signalcycle length model Based on the results of this study thefollowing conclusions were reached

(1) An optimization traffic signal cycle length model wasproposedUsing comprehensive delay data themodelfromWebster for optimal cycle time is re-recalibratedto the Chinese traffic conditions Not only does theoptimization model take the vehicle delay time intoconsideration but also the lower boundary consid-ered the factors of pedestrian crossing and the upperboundary considered the driversrsquo anxiety for waitinga long time which is related to traffic safety especiallyto risk-taking behavior

(2) The results of the microsimulation and cross-sec-tional analysis suggested that the difference in thedelay times and queue lengths of II and III signal-ized intersections with the optimization cycle lengthmodel was significantly smaller than that in the TRRLmodel It suggested that the optimization traffic signalcycle length model was more optimal than the TRRLmodel since it took the different traffic conditions ofthe intersections into consideration

The work presented in this paper provided insight intothe traffic signal cycle lengthmodel In China the traffic con-gestion at the intersection resulted in many problems suchas time delay air pollution and even traffic safety A mainreason for that is the unreasonable traffic signal cycle lengthFindings of this study provide an optimization traffic signalcycle length model considering the different traffic condi-tions These findings are helpful for traffic engineers andtraffic police to design a more reasonable cycle length for asignalized interaction given its traffic status

However there are several limitations in the presentstudyThe data used in the study was collected in one Chinesecity Similar studies should be done in other cities in China Inaddition the proposed traffic signal cycle time length modeldid not consider the effects of nonmotorized vehicles whichis mixed motorized vehicles at the intersections Future workwill focus on these two issues


Table 5 Summary statistics of queue length (vehiclesper cycle)


TRRL model Queue lengthI 120 14 0 274 279II 150 30 2 812 487III 180 38 3 1598 716

NEWmodel Queue lengthI 120 12 0 324 302II 150 25 2 604 366III 180 24 2 1002 439

Table 6 Results of 119905-tests for queue length


P valueTRRLmodel

NEWmodel

I Queue length 274 324 0184II Queue length 812 604 lt0001III Queue length 1598 1002 lt0001

Conflict of Interests

The authors declare that there is no conflict of interests

Acknowledgments

This research was sponsored by the National Natural ScienceFoundation of China (no 51478110) the Scientific ResearchFoundation of Graduate School of Southeast University (noYBJJ1458) the Fundamental Research Funds for the Cen-tral Universities and the Scientific Innovation Research ofCollege Graduates in Jiangsu Province (nos KYLX 0173 andKYLX 0174) The authors also would like to thank AssociateProfessor Bai for his beneficial advice and contribution to thepaper

References

[1] D Gerlough and A SchuhlUse of Poisson Distribution in High-way Traffic Eno Foundation for Highway Traffic Control 1955

[2] F Webster Traffic Signal Settings HMSO London UK 1958[3] F Webster and B Cobbe ldquoTraffic signalsrdquo Technical Paper 56

Ministry of Transport London UK 1966[4] R Akcelik Time-Dependent Expressions for Delay Stop Rate

and Queue Length at Traffic Signals Australian Road ResearchBoard Melbourne Australia 1980

[5] H Li D Wang and Z Qu ldquoResearch on the optimal methodof cycle length for signalized intersectionrdquo in Proceedings ofthe 8th International Conference on Applications of AdvancedTechnologies in Transportaion Engineering pp 371ndash376 May2004

[6] X Li G Li S-S Pang X Yang and J Tian ldquoSignal timingof intersections using integrated optimization of traffic qual-ity emissions and fuel consumption a noterdquo Transportation

Research Part D Transport and Environment vol 9 no 5 pp401ndash407 2004

[7] D Cheng Z Z Tian and C J Messer ldquoDevelopment of animproved cycle length model over the Highway Capacity Man-ual 2000 Quick Estimation Methodrdquo Journal of TransportationEngineering vol 131 no 12 pp 890ndash897 2005

[8] C M Day D M Bullock and J R Sturdevant ldquoCycle-lengthperformance measures revisiting and extending fundamen-talsrdquo Transportation Research Record vol 2128 pp 48ndash57 2009

[9] Transportation Research Board Highway Capacity ManualNational Research Council Washington DC USA 2010

[10] C-J Lan ldquoNew optimal cycle length formulation for pretimedsignals at isolated intersectionsrdquo Journal of Transportation Engi-neering vol 130 no 5 pp 637ndash647 2004

[11] L D Han and J-M Li ldquoShort or long-which is better Proba-bilistic approach to cycle length optimizationrdquo TransportationResearch Record Journal of the Transportation Research Boardvol 2035 pp 150ndash157 2007

[12] W Ma X Yang W Pu and Y Liu ldquoSignal timing optimizationmodels for two-stage midblock pedestrian crossingrdquo Trans-portation Research Record vol 2264 pp 133ndash144 2010

[13] T-H Chang and J-T Lin ldquoOptimal signal timing for anoversaturated intersectionrdquo Transportation Research Part BMethodological vol 34 no 6 pp 471ndash491 2000

[14] R Putha L Quadrifoglio and E Zechman ldquoComparing antcolony optimization and genetic algorithm approaches for solv-ing traffic signal coordination under oversaturation conditionsrdquoComputer-AidedCivil and Infrastructure Engineering vol 27 no1 pp 14ndash28 2012

[15] L Zhao X Peng L Li and Z Li ldquoA fast signal timing algorithmfor individual oversaturated intersectionsrdquo IEEE Transactionson Intelligent Transportation Systems vol 12 no 1 pp 280ndash2832011

[16] D Ma and H Nakamura ldquoCycle length optimization at isolatedsignalized intersections from the viewpoint of emissionrdquo Trafficand Transportation Studies vol 383 pp 275ndash284 2010

[17] B Park N M Rouphail and J Sacks ldquoAssessment of stochasticsignal optimization method using microsimulationrdquo Trans-portation Research Record vol 1748 pp 40ndash45 2001

[18] J Kim J Lee and M Chang ldquoPerformance comparisonbetween artificial neural network and analytical models forreal-time cycle length designrdquo Transportation Research RecordJournal of the Transportation Research Board vol 1988 pp 102ndash115 2006

[19] X-G Yang J Zhao and T Wang ldquoOptimal cycle calculationmethod of signal control at roundaboutrdquoChina Journal of High-way and Transport vol 21 no 6 pp 90ndash95 2008


[20] R Akcelik Traffic Signals Capacity and Timing Analysis Aus-tralian Road Research Board Melbourne Australia 1981

[21] S Washington M Karlaftis and F Mannering Statistical andEconometric Methods for Transportation Data Analysis Chap-man amp Hall Washington DC USA 2003

Submit your manuscripts athttpwwwhindawicom

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Differential EquationsInternational Journal of

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Applied MathematicsJournal of


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Journal of


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OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


TheARRBmodel [4] introduced the ldquoparking compensa-tion coefficientrdquo to the TRRLmodel and it was combinedwiththe vehicle delay time to evaluate the degree of optimizationof the signal timing program The ARRB model is given as

1198880=

(14 + 119896) + 6

1 minus 119884

(2)


sents the parking compensation coefficient and 119884 representssum of the critical flow ratio of all phases

Although the above models are widely used they havesome limitations (1) under near-saturated or saturated con-ditions the optimal cycle length formulation proposed byWebster becomes infeasible because it generates an unreason-ably large cycle length as the intersection critical flow ratioapproaches one (2) it becomes inapplicable if the intersectioncritical flow ratio is equal to or greater than one

The Highway Capacity Manual [9] also proposed thecycle length model and the delay time model of signalizedintersections The delay time model which can be applied tovariety of saturation states has been widely used The cyclelength model is based on the expected saturation thereforeit does not guarantee that the cycle length would produce theminimum delay at an intersection It is given as

119862 =

119871

1 minus [min (CSRS) RS] (3)

where 119862 represents the cycle length (sec) 119871 represents thetotal lost time (seccycle) CS represents the sumof the criticalphase traffic volumes (vehh) RS represents the referencesum flow rate (1710lowastPHFlowastfa) (vehh) PHF represents thepeak-hour factor and fa represents the area type adjustmentfactor [09 if central business district and 10 otherwise]

Day et al [8] evaluated the effectiveness and efficiency ofWebsterrsquos cycle length and the HCM intersection saturationmetric The authors showed that calculations fromWebsterrsquosmodel and the HCM provided a framework for identifyingperiods of time when the cycle length could be substantiallyshortened periods of the day when an increase in thecycle length would provide some modest improvements andperiods of the day when the cycle length was adequate andcapacity problems could be addressed by adjusting the splitsA similar study conducted by Cheng et al [7] comparedWebsterrsquos minimum delay cycle length model and the HCM2000 optimal cyclemodel and recommended an exponential-type cycle length model

Based on the idea of minimizing the delay time manyoptimization cycle length models were developed usinglinear or nonlinear regression methods and probabilisticapproaches among others [10ndash12] Lan [10] proposed anonlinear optimal cycle length Using the optimal timingvariables obtained based on the delayminimization criterionthe functional relationship between the optimal cycle lengthsand the traffic flow parameters including the intersectioncritical flow ratio the total lost time and the duration ofthe analysis period was established through a nonlinear

regression analysis The formulation was found to generatefairly accurate estimates of optimal cycle length with a57 average deviation from the analytical solutions Hanand Li [11] studied a probabilistic approach to cycle lengthoptimization Based on the idea of selecting a cycle lengththat is small enough to ensure low delay while providingadequate capacity to handle most of the fluctuating demandconditions a five-step framework was proposed for carryingout the analyses Subsequent sensitivity analyses level-of-service assessments and cycle failure rate estimations wereconducted on the basis of random demand It was found thatlonger cycle lengths did not yield the optimal delay resultsand with extremely short cycle lengths the delay was usuallyhigh because of a lack of capacity and hence frequent cyclefailures were guaranteed

A second class of methods is based on studies aimed atoptimizing the cycle length for a saturated or oversaturatedintersection [13ndash15] Chang and Lin [13] studied the optimalsignal timing for an oversaturated intersection The authorspresented a timing decision methodology which considersthe whole oversaturation period and discrete dynamic opti-mization models were developed The optimal cycle lengthand the optimal assigned green time for each approach weredetermined for the case of two-phase control It was foundthat the proposed discrete type performance index model isa more appropriate design for congested traffic signal timingcontrol

A third class of methods is based on taking the factor ofemissions fuel and other environmental factors into consid-eration when developing the cycle length model [5 6 16] Liet al [5 6] established a signal timingmodel which optimizessignal cycle length and green time by using integratedoptimization of the traffic quality fuel consumption andemission pollution It was found that when the signal cyclelength increased from 20 to 200 s there was an optimal valuecorresponding to the performance index function When thetraffic flow rate was larger the optimal signal cycle lengthcorresponding to the performance index function increasedHowever the parameters of the model are complicated anddifficult to obtain and is therefore useful for the purpose ofstudy only and is not practical in engineering practice

The fourth class of methods is based on simulation andan intelligent algorithm to optimize the cycle length or todevelop an optimization cycle length model [17ndash19] Usingthe theory analysis and computer simulation test Yang et al[19] established a delaying calculation model of through run-ning and left-turning vehicles on a roundabout Based on themodel an optimal cycle length calculation method targetingminimum delay was derived which was suitable for the mul-tiapproach going in coordination with roundabout controlsPark et al [17] evaluated a stochastic signal optimizationmethod based on a genetic algorithm using the microscopicsimulation program CORSIM According to the method thecycle length the green ratio and the phase difference wereoptimized at the same time Kim et al [18] compared theperformance between an artificial neural network (ANN) andanalytical models for real-time cycle length design It wasfound that the ANN model provides optimal cycle lengthsstably adjusted by the minimum value the maximum value





2 Data Collection







119863 = 119873 lowast 119905

119889 =

119863

119881

(4)



120582 =

119892

119862

(5)



119909119894=

119902119894

120582119894119904119894

(6)

119883 = max 119909119894 119894 = 1 2 3 119899 (7)


119894represents


119894represents














119889 = 1205721198891+ 1205731198892+ 1205741198893

1198891=

119862 (1 minus 120582)2

2 (1 minus 120582119909)

1198892=

1199092

2119902 (1 minus 119909)

1198893= minus065 (

119862

1199022)

13

1199092+5120582

(8)






119889119894= 116

119862 (1 minus 120582119894)2

2 (1 minus 120582119894119909119894)

+ 066

1199092

119894

2119902119894(1 minus 119909

119894)

minus 079(

119862

1199022

119894

)

13

1199092+5120582119894

119894

(9)


120582119894=

119892119894

119862

=

119862 minus 119871

119862

119910119894

119884

= (1 minus

119871

119862

)

119910119894

119884

(10)





119909119894=

119902119894

120582119894119904119894

=

119902119894

119904119894(1 minus 119871119862) (119910

119894119884)

=

119910119894

(1 minus 119871119862) (119910119894119884)

=

119884

(1 minus 119871119862)

(11)


119889119894= 116

119862 (1 minus 120582119894)2

2 (1 minus 119910119894)

+ 066

(119884 (1 minus 119871119862))2

2119902119894(1 minus 119884 (1 minus 119871119862))

minus 079(

119862

1199022

119894

)

13

(

119884

1 minus 119871119862

)

2+5120582119894

(12)



119902119894119889119894 (13)


Phase one

Phase two

Phase one Phase one

Phase two

Phase two


Cuih

ua R

d

Xiaozhai Rd

Phase four

FengchengFive Rd

Nor

thTa

ihua

Rd


Rd

Sout

h Ta

ibai

Rd

(I) (II) (III)







119862 =

145119871 + 3

1 minus 119884

(14)




119862 =

145119871 + 3

1 minus 119884




119892min = 7 +119871119901

V119901

(16)


119862min = sum119894

(7 +

119871119901

V119901

) + 119871 (17)







119862 =

145119871 + 3

1 minus 119884


with

119862min = sum119894

(7 +

119871119901

V119901

) + 119871

119862max = 180

(19)




119892119894= 119892min119894 = 7 +

119871119901119894

V119901119894

for 119888 = 119862min

119892119894= (119862 minus 119871)

119910119894

119884


(20)



















119905 =

100381610038161003816100381610038161198831minus 1198832

10038161003816100381610038161003816

radic1199042

11198991+ 1199042

21198992

ge 1199051205722 (21)


2are the average






df =(1199042

11198991+ 1199042

21198992)

2

(1199042

11198991)2 (1198991minus 1) + (119904

2

21198992)2 (1198992minus 1)

(22)












P valueTRRLmodel

NEWmodel



















P valueTRRLmodel

NEWmodel




Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













2 Data Collection







119863 = 119873 lowast 119905

119889 =

119863

119881

(4)



120582 =

119892

119862

(5)



119909119894=

119902119894

120582119894119904119894

(6)

119883 = max 119909119894 119894 = 1 2 3 119899 (7)


119894represents


119894represents














119889 = 1205721198891+ 1205731198892+ 1205741198893

1198891=

119862 (1 minus 120582)2

2 (1 minus 120582119909)

1198892=

1199092

2119902 (1 minus 119909)

1198893= minus065 (

119862

1199022)

13

1199092+5120582

(8)






119889119894= 116

119862 (1 minus 120582119894)2

2 (1 minus 120582119894119909119894)

+ 066

1199092

119894

2119902119894(1 minus 119909

119894)

minus 079(

119862

1199022

119894

)

13

1199092+5120582119894

119894

(9)


120582119894=

119892119894

119862

=

119862 minus 119871

119862

119910119894

119884

= (1 minus

119871

119862

)

119910119894

119884

(10)





119909119894=

119902119894

120582119894119904119894

=

119902119894

119904119894(1 minus 119871119862) (119910

119894119884)

=

119910119894

(1 minus 119871119862) (119910119894119884)

=

119884

(1 minus 119871119862)

(11)


119889119894= 116

119862 (1 minus 120582119894)2

2 (1 minus 119910119894)

+ 066

(119884 (1 minus 119871119862))2

2119902119894(1 minus 119884 (1 minus 119871119862))

minus 079(

119862

1199022

119894

)

13

(

119884

1 minus 119871119862

)

2+5120582119894

(12)



119902119894119889119894 (13)


Phase one

Phase two

Phase one Phase one

Phase two

Phase two


Cuih

ua R

d

Xiaozhai Rd

Phase four

FengchengFive Rd

Nor

thTa

ihua

Rd


Rd

Sout

h Ta

ibai

Rd

(I) (II) (III)







119862 =

145119871 + 3

1 minus 119884

(14)




119862 =

145119871 + 3

1 minus 119884




119892min = 7 +119871119901

V119901

(16)


119862min = sum119894

(7 +

119871119901

V119901

) + 119871 (17)







119862 =

145119871 + 3

1 minus 119884


with

119862min = sum119894

(7 +

119871119901

V119901

) + 119871

119862max = 180

(19)




119892119894= 119892min119894 = 7 +

119871119901119894

V119901119894

for 119888 = 119862min

119892119894= (119862 minus 119871)

119910119894

119884


(20)



















119905 =

100381610038161003816100381610038161198831minus 1198832

10038161003816100381610038161003816

radic1199042

11198991+ 1199042

21198992

ge 1199051205722 (21)


2are the average






df =(1199042

11198991+ 1199042

21198992)

2

(1199042

11198991)2 (1198991minus 1) + (119904

2

21198992)2 (1198992minus 1)

(22)












P valueTRRLmodel

NEWmodel



















P valueTRRLmodel

NEWmodel




Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














119889 = 1205721198891+ 1205731198892+ 1205741198893

1198891=

119862 (1 minus 120582)2

2 (1 minus 120582119909)

1198892=

1199092

2119902 (1 minus 119909)

1198893= minus065 (

119862

1199022)

13

1199092+5120582

(8)






119889119894= 116

119862 (1 minus 120582119894)2

2 (1 minus 120582119894119909119894)

+ 066

1199092

119894

2119902119894(1 minus 119909

119894)

minus 079(

119862

1199022

119894

)

13

1199092+5120582119894

119894

(9)


120582119894=

119892119894

119862

=

119862 minus 119871

119862

119910119894

119884

= (1 minus

119871

119862

)

119910119894

119884

(10)





119909119894=

119902119894

120582119894119904119894

=

119902119894

119904119894(1 minus 119871119862) (119910

119894119884)

=

119910119894

(1 minus 119871119862) (119910119894119884)

=

119884

(1 minus 119871119862)

(11)


119889119894= 116

119862 (1 minus 120582119894)2

2 (1 minus 119910119894)

+ 066

(119884 (1 minus 119871119862))2

2119902119894(1 minus 119884 (1 minus 119871119862))

minus 079(

119862

1199022

119894

)

13

(

119884

1 minus 119871119862

)

2+5120582119894

(12)



119902119894119889119894 (13)


Phase one

Phase two

Phase one Phase one

Phase two

Phase two


Cuih

ua R

d

Xiaozhai Rd

Phase four

FengchengFive Rd

Nor

thTa

ihua

Rd


Rd

Sout

h Ta

ibai

Rd

(I) (II) (III)







119862 =

145119871 + 3

1 minus 119884

(14)




119862 =

145119871 + 3

1 minus 119884




119892min = 7 +119871119901

V119901

(16)


119862min = sum119894

(7 +

119871119901

V119901

) + 119871 (17)







119862 =

145119871 + 3

1 minus 119884


with

119862min = sum119894

(7 +

119871119901

V119901

) + 119871

119862max = 180

(19)




119892119894= 119892min119894 = 7 +

119871119901119894

V119901119894

for 119888 = 119862min

119892119894= (119862 minus 119871)

119910119894

119884


(20)



















119905 =

100381610038161003816100381610038161198831minus 1198832

10038161003816100381610038161003816

radic1199042

11198991+ 1199042

21198992

ge 1199051205722 (21)


2are the average






df =(1199042

11198991+ 1199042

21198992)

2

(1199042

11198991)2 (1198991minus 1) + (119904

2

21198992)2 (1198992minus 1)

(22)












P valueTRRLmodel

NEWmodel



















P valueTRRLmodel

NEWmodel




Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Phase one

Phase two

Phase one Phase one

Phase two

Phase two


Cuih

ua R

d

Xiaozhai Rd

Phase four

FengchengFive Rd

Nor

thTa

ihua

Rd


Rd

Sout

h Ta

ibai

Rd

(I) (II) (III)







119862 =

145119871 + 3

1 minus 119884

(14)




119862 =

145119871 + 3

1 minus 119884




119892min = 7 +119871119901

V119901

(16)


119862min = sum119894

(7 +

119871119901

V119901

) + 119871 (17)







119862 =

145119871 + 3

1 minus 119884


with

119862min = sum119894

(7 +

119871119901

V119901

) + 119871

119862max = 180

(19)




119892119894= 119892min119894 = 7 +

119871119901119894

V119901119894

for 119888 = 119862min

119892119894= (119862 minus 119871)

119910119894

119884


(20)



















119905 =

100381610038161003816100381610038161198831minus 1198832

10038161003816100381610038161003816

radic1199042

11198991+ 1199042

21198992

ge 1199051205722 (21)


2are the average






df =(1199042

11198991+ 1199042

21198992)

2

(1199042

11198991)2 (1198991minus 1) + (119904

2

21198992)2 (1198992minus 1)

(22)












P valueTRRLmodel

NEWmodel



















P valueTRRLmodel

NEWmodel




Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

























119905 =

100381610038161003816100381610038161198831minus 1198832

10038161003816100381610038161003816

radic1199042

11198991+ 1199042

21198992

ge 1199051205722 (21)


2are the average






df =(1199042

11198991+ 1199042

21198992)

2

(1199042

11198991)2 (1198991minus 1) + (119904

2

21198992)2 (1198992minus 1)

(22)












P valueTRRLmodel

NEWmodel



















P valueTRRLmodel

NEWmodel




Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















P valueTRRLmodel

NEWmodel



















P valueTRRLmodel

NEWmodel




Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















P valueTRRLmodel

NEWmodel




Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article development of an optimization traffic...

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