estimation of origin destination matrix – a case study of

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 08 Issue: 06 | June 2021 www.irjet.net p-ISSN: 2395-0072

© 2021, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 2219

Estimation of Origin Destination Matrix – A Case Study of Kolkata

Sayangdipto Chakraborty1, Subhra Chakravorty2, Pritha Banerjee3

1-3Department of Computer Science & Engineering, University of Calcutta, Kolkata, West Bengal, India ---------------------------------------------------------------------***---------------------------------------------------------------------Abstract - The demand of mobility has increased significantly all over the world due to rapid urbanisation. The situation in India is no different and Kolkata with 6% road space ends up as one of the most congested metropolitan cities. Thus, an efficient public transportation system is needed to reduce the congestion on road. In this paper we have estimated Origin Destination matrix of the city using standard Gravity Model. The supply or the current bus trip data has been obtained from the state transport application’s database and the estimated origin destination matrix has been obtained using the Gravity Model to assess the demand.

Key Words: Gravity Model, Origin Destination Matrix, Transportation Forecasting, Trip Distribution, Urban Planning, Trip Generation, Transportation Engineering

1. INTRODUCTION Urbanisation refers to the population shift from rural to urban areas. This is characterized by huge traffic growth in the cities along with shortage of adequately maintained road space. The situation is serious in cities of India where the area is limited, population density huge and roads not built for the future. In India, the share of public transportation peaks among people living in the megalopolis regions, where the supply networks and systems are inappropriate. The problem is acute in the Indian city of Kolkata as the road space here is only 6% compared to 23% in Delhi and 17% in Mumbai. In addition, the layout of Kolkata does not allow much scope for widening of roads unlike other metropolitan cities of India. Therefore, the need arises to do a transportation forecasting based on the current supply of public buses on the road network of Kolkata.

In this paper, we have divided Kolkata into different zones and then observed the movement and frequency of public buses in these zones from public servers. From the observed data we have estimated the demand. This essentially will help us estimate the gap in the supply and required demand of public transportation for each zone.

2. LITERATURE REVIEW Transportation Forecasting [1] is the attempt of estimating the number of vehicles or people that will use a specific transportation facility in the future. For instance, a forecast may estimate the number of vehicles on a planned road or bridge, the number of passengers on a route. Traffic forecasting begins with the collection of data on current traffic. This traffic data is combined with other known data, such as population, employment, trip rates, travel costs, etc., to develop a traffic demand model for the current situation.

Feeding it with predicted data for population, employment, etc. results in estimates of future traffic, typically estimated for each segment of the transportation infrastructure in question which is the roadway segment

Within the rational planning framework, transportation forecasts have traditionally followed the sequential four-step model. The four steps of the classical urban transportation planning system model are:

Trip generation. The movement between an origin destination pair is counted as a trip. This step determines the frequency of trips between origin destination pairs.

Trip distribution connects the generated trips between origin and destination zones using some trip distribution model.

Mode choice computes the proportion of trips between each origin and destination that uses a particular mode of transportation.

Route assignment assign routes in order to satisfy the demand of trips given in the Origin Destination matrix of a particular mode of transport.

Our area of focus is the Trip Generation and Trip Distribution of the traditional four-step transportation forecasting model. In Trip Generation step, multiple surveys are conducted to obtain the count of traffic movement between pairs of zone. These surveys can be physical using traffic sensors or camera or virtual from servers providing live data. Using the data, an observed origin destination matrix is created. The next step is Trip Distribution step creates a “trip table”, a matrix that estimates number of trips for each origin destination pair. From the observed Trip Matrix using traffic forecasting models we can obtain the estimated Origin Destination Matrix to assess the requirements. Historically, the latter component has been the least developed component of the transportation planning model. In [2] we get a detailed theoretical analysis of all trip distribution models. Largely, the models can be classified into two categories: Growth Factor Methods or Synthetic Methods. The growth factor methods use past and current data to estimate the growth factor over a period and then estimate the future growth with that growth factor. Growth factor methods assume that in the future the trip making pattern will remain substantially the same as today but that the volume of trips will increase according to the growth of the generating and attracting zones. These methods are simpler than synthetic methods and for small towns where



© 2021, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | 220

considerable changes in land use and external factors are not expected, they have often been considered adequate.

O D 1 2 3 Oi

1 T11 T12 T13 O1

2 T21 T22 T23 O2

3 T31 T32 T33 O3

Dj D1 D2 D3 Ʃij Tij

Table -1: Illustrative Origin Destination Matrix. Here, Tij

represents the number of trips from origin (O) in zone i to destination (D) in zone j. Oi represents the number of trips

originating or the production from zone i, Dj represents the number of trips terminating at zone j or the attraction

of zone j

The Constant Factor Method[2][4], Doubly Constrained Growth Factor Model introduced by Furness[2][4], Average Factor Methods[2] and the Fratar Method[2] are some of the growth factor methods which suffer from disadvantages of reliance on current and past data to estimate the future when in reality the situation may not be so linear.

To the best of our knowledge, there is no Origin Destination study available for Kolkata. This motivates the study of the Origin Destination matrix in this paper towards modeling an optimized public transport network for the city of Kolkata.

2.1 Gravity Model [3][4] The idea of gravity method originally came from Newton’s Universal Gravitational Law. The simplest expression of the model has the following functional form:

Here, Pi and Pj are the populations of the origin and destination, dij is the distance between origin and destination respectively, and α was a proportional factor. This gravity model was not ready to use for transportation purpose. So, some improvements were applied including the use of total trips instead of population and several other parameters to calibrate the model. After the improvements, the gravity model for transportation could be used for transportation purposes. The formulation of gravity model for transportation is shown below.

----- (1)

Here Tij is the number of trips from zone i to zone j, Oi is the number of trips originating at zone i, Dj is the number of trips terminating at zone j, f(cij) is the deterrence function, Ai

and Bj are balancing factors. cij is the cost matrix value between zone i and zone j. The value of c depends on various factors such as distance, speed, fare, time, comfort etc.

----- (2)

----- (3)

The deterrence function can be written as:

----- (4)

The deterrence function is affected by the value of β. Higher value of β implies lower average trip cost. There are some calibration techniques to get the correct value of β, such as the Hyman method.

2.1 Hyman Calibration Method [5] The Hyman method is one of the techniques used to calibrate the parameter in the deterrence functions. The Hyman method was found to be more robust and effective than other calibration techniques. The steps to estimate β are as follows.

----- (5)

The initial mean cost from observation is calculated as:

----- (6)

The Hyman method can be described as follows: 1. The first iteration starts by making iteration

number m=0 and an initial estimate of 𝛽0 = 1/c*. 2. Using this value of β0 the new origin destination

matrix is calculated using the standard gravity model. The mean trip cost c0 is obtained again using (6) and a better value of β is estimated as follows:

----- (7)

3. Make m = m+1. Using the latest value for , an origin destination matrix using standard gravity model is calculated again and the new mean trip cost cm-1 is obtained and compared with c*. If they are sufficiently close, the iteration is stopped and m-1 is accepted as the best estimate for this parameter; otherwise we move to step 4.

4. The better estimate of is obtained as:

5. Steps 3 and 4 are continued as necessary, that is, until the last mean cost cm-1 is sufficiently close to the observed value of c* .

3. METHODOLOGY Data Collection: An integral part of the project was collecting data. Given the physical limitations of live surveys we chose to use the West Bengal Public Transport Application [6] to obtain all the data.




Fig-1: The Pathadisha App to track buses.

The application is freely available in the Google Play Store or iOS App Store and the end point URLs to obtain the data is available open source on GitHub. Using this, we obtained 1341 bus routes moving in and out of Kolkata or its close

adjoining areas. We also obtained a list of 1819 stoppages which are classified as TERMINAL, JUNCTION or STOP shown in Figure 2. Further the latitude and longitude of these stoppages are also available in the data.

Fig-2: A snapshot of the stoppages

Zonal Division of Kolkata: The next part included dividing Kolkata into Zones to track the movement of buses. We considered the same ten zones from [7] along with three

additional zones to include Dum Dum Municipal Area, Rajarhat area and Howrah municipal Area as shown in the table 2.

Zone

Number

Administrative Boundary Region

Borough Ward Number

1 I 1,2,3,4,5,6,7,8,9 Bagbazar, Belgachia, Paikpara,

Chitpur, Sinthi

2 II & IV 10,11,1215,16,17,18,19, 20,21,22,23,24,25,26,27,

28,38

Shyambazar, Shovabazar, Girish

Park, Barabazar

3 III 13,14,29,30,31,32,33,34,35 Ultadanga, Manicktala,

Narkeldanga, Beliaghata

4 V, VI & VII

(partial)

36,37,39,40,41,42,43,44,45,

48,49,50,46,47,51,52,53,54, 55,60,61,62,63

BBD Bag, Sealdah, Esplanade,

Maidan

5 VII (majority) 56,57,58,59, 64,65,66,67 Tangra, Kustia, Dhapa, Tiljala,

Kasba

6 VIII 68,69,70,71,72,73,84,85,86, 87,90 Bhawanipur, Ballygaunge, Gariahat,




Golpark

7 IX & XV 74,75,76,77,78,79,80,82,83,

88,133,134,135,136,137,138, 139,140,141

Khidirpur, Garden Reach, Alipur,

Chetla

8 X & XI 81,89,91,92,93,94,95,96,97,98,

99,100,101,102,110,111,112, 113,114

Jadavpur, Tollygaunge, Baghajatin,

Garia

9 XII 103,104,105,106,107,108,109 Haltu, Mukundapur, Santoshpur,

Ajaynagar

10 XIII & XIV 115,116,117,118,119,120,121,

122,123,124,125,126,127,128, 129,130,131,132

Behala Purba, Behala Paschim,

Thakurpukur

11 Bidhannagar Municipality (Northern), North Dum Dum Municipality,

Madhyamgram Municipality

Airport Area, North Dum Dum,

Barrackpore, Barasat

12 Bidhannagar Municipality (Southern), Newtown Kolkata

Development Authority (NKDA)

Salt Lake, Kestopur,

Hatiara,Newtown, Baguiati,

Rajarhat

13 Howrah Municipal Corporation Howrah District

Table-2: Division of Kolkata into Zones.

Classification of Bus Trips to Zones: Now for each zone, several important stops are considered that cover the entire area of the zone. So that when buses are tracked at each of these stoppages, all the buses moving in or out of the zone is obtained without a miss. Further, since we also obtain the vehicle numbers from the data there is no chance of counting a bus twice in a zone. For each bus route, the terminating stoppage was considered and it was classified into one of the 13 zones as above. For example, a bus terminating or going to Sealdah will have its end zone number as 4. A sink end zone 0 was considered for all buses

terminating at places not covered in any of our 13 zones. We have ignored this sink vertex in our calculation of the origin destination matrix. This includes WBSTC buses going to faraway places like Digha or Nadia. Figure 3 shows a snapshot of the data after the bus routes have been classified into zones. The obtained buses at each zone were then classified as per Figure 3 into the zones they were going to as per Table 2. Figure 4 shows a snapshot of the buses observed at zone 1 and classified into end zones as per Table 2.

Fig-3: Snapshot of Bus Routes classified into End Zones.




Fig-4: Snapshot of buses obtained at a zone and classified into end zones.

After the classification all buses available in the database into their end zones, the next task was to obtain the buses moving in a particular zone. For all the stoppages in a given zone i, we obtained the buses at those points in intervals of two minutes for a duration of 20 minutes. For each zone from 1 to 13, the buses at that zone were obtained in a fixed 20 minute period during peak office hours. Based on the classification into end zones, we obtained the number of buses travelling from zone i to zone j as is required for generating the origin destination matrix. We ignored the count of sink vertex 0 as stated previously and obtained the final 13 x 13 observed Origin Destination matrix as shown in Figure 6.

Calculation of Cost Matrix: The next part of the project included calculation of the cost matrix C [4]. This cost element may be considered in terms of distance, time or money units. It is often convenient to use a measure combining all the main attributes related to the dis-utility of a journey and this is normally referred to as the generalized cost of travel. We have already obtained the speed of travel of each bus and therefore we get the mean speed of travel in the entire city. This comes as 19.07km/h. To calculate the cost function, we needed distance, travel time and cost of movement between zones. The distance was

calculated taking the distance between the central points of each zone. We have already obtained the average speed as 19.07 km/h. Therefore, the travel times between zones can also be calculated as Time = Distance/Speed. To calculate each trip cost an assumption was taken that 90% of the buses on route are Non-AC while the rest 10% of the buses are AC. The weighted average of the fares were taken based on distances. For example, the fare to travel 4 kms is ₹7 in a non-AC bus and ₹25 in an AC bus, the weighted average of these two fares ₹8.8 is considered as fare to travel up to 4kms. Travelling in the same zone accounts for least cost of ₹8.8. For others based on distance the average cost has been considered.

The final cost matrix C is calculated as a linear equation of the form:

Here, dij refers to the distance between zones i and j, tij refers to the time taken to travel from zone i to zone j and fij refers to the fare charged to travel between zone i and j. a1, a2 and a3 are the weights attached to each of these figures. Since both tij and fij are invariably related to dij, we can assume that a1, a2 and a3 are equal and add up to 1. So, the final cost matrix C as obtained is shown in Figure 5.

Fig-5: Calculated Cost Matrix. a1 = a2 = a3 = 1/3 are weights assigned to the three factors




4. RESULTS & DISCUSSIONS Trip Generation: Using the data from the servers, the following origin destination matrix was observed in 20

minutes during peak office hours. It is to be remembered that the data was collected right before lockdown during peak COVID-19 pandemic and therefore maybe biased.

Fig-6: The observed Origin Destination Matrix. The number of buses Tij moving from Origin (O) in Zone i to Destination (D) in Zone j in 20 minutes. Oi refers to the numbers of buses originating at a zone i while Dj refers

to the number of buses going to zone j.

Trip Distribution & Estimation: The standard gravity model was implemented using Hyman Calibration Method for the above observed trip matrix in Figure 6. From the

iterative calibration technique the value of β was obtained as 0.0487 and the corresponding Origin Destination Matrix was obtained as shown in Figure 7.

Fig-7: Gravity Model using Hyman Calibration Technique. β = 0.0487




Discussions: The study estimated the number of bus trips in the morning for the region of greater Kolkata. The demand matrix is obtained as shown in Fig-7 from the supply matrix as shown in Fig-6.The total demand deviation calculated as difference between observed ƩijTij from the estimated ƩijTij is obtained as 6.57%. However, considering only zone 1-10 as the Origin Destination Matrix this deviation would have been reduced to 2.82%. This difference can be probably attributed to the biased data obtained due to lockdown for zone 11, 12 and 13. Trip Distribution was also implemented by methods other than Hyman Method. The total demand deviation was obtained as 11.41% and 23.09% for these ineffiecient power models. More such estimations could have been done at several time intervals of the day to obtain better results. Further, if we look at the productions (Oi) and the attractions (Dj) the values are close to the observed values for most zones except Zone 4. Zone 4 consists of Central Kolkata where the mobility is very high and therefore the demand for buses originating or terminating is also high in that region. It is clear that for most zones supply is being met, but for zones like 4 the demand exceeds the supply. It is to be remembered that the data was collected during the pandemic and therefore the data may not fully account for the situation in normal days. But the methodology used will be the same. The calibration parameter as obtained from the Hyman model is β = 0.0487. For the further study, the value of β can be used for estimating the origin destination matrix of Kolkata city in future.

4. CONCLUSIONS A successful case study of Trip Generation and Trip Distribution was conducted for Kolkata. With the help of data from servers the observed Origin Destination Matrix for 20 minutes in the office hours of a weekday was obtained. Using that data and some other information we created a cost matrix that led us to estimate the demand Origin Destination Matrix. This would be extremely useful for proper transport planning of the city. This study can be done at different intervals of the day to estimate the demand from supply based on movement to or from zones of attraction. For example, Salt Lake Area maybe an attraction in morning office hours but becomes a zone of production in the evening hours. Such information helps meet public demand readily. Further, Trip Distribution Matrix has to be created for population movement, that is, number of people moving from one zone to another. In the coming years traffic is expected to grow substantially in response to the mobility needs of the expanding population. Given the limited road space in the core city areas, this vehicular growth will lead to acute congestion in most of the Indian cities. To deal with these problems steps have to be taken, including optimisation of routes and bus networks based on demand and supply. Public travel demand has to be met with proper supply which can be estimated from techniques like these. This will also help in

removal of redundant routes and allocating new routes. Beyond public transport, private vehicles also have to be considered for estimations. Urban planning of cities have to be based on these methodologies.

REFERENCES [1] Wikipedia: Transportaion Forecasting. Retrieved: June,

2021. https://bit.ly/3vaCz9Z

[2] Salter R.J. 1989 Trip distribution. In: Highway Traffic Analysis and Design. Palgrave, London. Springer

[3] I Ekowicaksono, F Bukhari and A Aman 2016 IOP Conference Series: Earth and Environmental Science Volume 31. Estimating Origin-Destination Matrix of Bogor City Using Gravity Model

[4] Trip distribution Chapter 8, NPTEL Published: May, 2007. Retrieved: June, 2021. https://bit.ly/3glol0x

[5] G M Hyman 1969. The Calibration of Trip Distribution Models. London Environment and Planning pp 105-112

[6] Pathadisha App on Google Play. https://bit.ly/2TMBibU

[7] Tuhin Subhra Maparu and Debapratim Pandit 2010. Institute of Town Planners, India Journal. A Methodology for Selection of Bus Rapid Transit Corridors: A Case Study of Kolkata

[8] Wikipedia: Trip Distribution. Retrieved: June, 2021. https://bit.ly/35qQqhN

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