Estimation of Origin Destination Matrix – a Case Study of Kolkata

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

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 Feeding it with predicted data for population, employment, significantly all over the world due to rapid urbanisation. The etc. results in estimates of future traffic, typically estimated situation in India is no different and Kolkata with 6% road for each segment of the transportation infrastructure in space ends up as one of the most congested metropolitan question which is the roadway segment cities. Thus, an efficient public transportation system is needed Within the rational planning framework, transportation to reduce the congestion on road. In this paper we have forecasts have traditionally followed the sequential four-step estimated Origin Destination matrix of the city using standard model. The four steps of the classical urban transportation Gravity Model. The supply or the current bus trip data has planning system model are: been obtained from the state transport application’s database  Trip generation. The movement between an origin and the estimated origin destination matrix has been obtained destination pair is counted as a trip. This step using the Gravity Model to assess the demand. determines the frequency of trips between origin destination pairs. Key Words: Gravity Model, Origin Destination Matrix, Transportation Forecasting, Trip Distribution, Urban  Trip distribution connects the generated trips Planning, Trip Generation, Transportation Engineering between origin and destination zones using some trip distribution model. 1. INTRODUCTION  Mode choice computes the proportion of trips between each origin and destination that uses a Urbanisation refers to the population shift from rural to particular mode of transportation. urban areas. This is characterized by huge traffic growth in  Route assignment assign routes in order to satisfy the cities along with shortage of adequately maintained road the demand of trips given in the Origin Destination space. The situation is serious in cities of India where the area matrix of a particular mode of transport. is limited, population density huge and roads not built for the future. In India, the share of public transportation peaks Our area of focus is the Trip Generation and Trip among people living in the megalopolis regions, where the Distribution of the traditional four-step transportation supply networks and systems are inappropriate. The problem forecasting model. In Trip Generation step, multiple surveys is acute in the Indian city of Kolkata as the road space here is are conducted to obtain the count of traffic movement only 6% compared to 23% in Delhi and 17% in Mumbai. In between pairs of zone. These surveys can be physical using addition, the layout of Kolkata does not allow much scope for traffic sensors or camera or virtual from servers providing widening of roads unlike other metropolitan cities of India. live data. Using the data, an observed origin destination Therefore, the need arises to do a transportation forecasting matrix is created. The next step is Trip Distribution step based on the current supply of public buses on the road creates a “trip table”, a matrix that estimates number of trips network of Kolkata. for each origin destination pair. From the observed Trip In this paper, we have divided Kolkata into different zones Matrix using traffic forecasting models we can obtain the and then observed the movement and frequency of public estimated Origin Destination Matrix to assess the buses in these zones from public servers. From the observed requirements. Historically, the latter component has been data we have estimated the demand. This essentially will help the least developed component of the transportation us estimate the gap in the supply and required demand of planning model. public transportation for each zone. 2. LITERATURE REVIEW 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 Transportation Forecasting [1] is the attempt of estimating the number of vehicles or people that will use a specific Methods. The growth factor methods use past and current transportation facility in the future. For instance, a forecast data to estimate the growth factor over a period and then may estimate the number of vehicles on a planned road or estimate the future growth with that growth factor. Growth bridge, the number of passengers on a route. Traffic factor methods assume that in the future the trip making forecasting begins with the collection of data on current pattern will remain substantially the same as today but that traffic. This traffic data is combined with other known data, the volume of trips will increase according to the growth of such as population, employment, trip rates, travel costs, etc., the generating and attracting zones. These methods are to develop a traffic demand model for the current situation. simpler than synthetic methods and for small towns where

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 considerable changes in land use and external factors are not expected, they have often been considered adequate. ----- (3)

D 1 2 3 O O i The deterrence function can be written as: 1 T11 T12 T13 O1 ----- (4) 2 T21 T22 T23 O2 The deterrence function is affected by the value of β. Higher 3 T31 T32 T33 O3 D D D D Ʃ T value of β implies lower average trip cost. There are some j 1 2 3 ij ij calibration techniques to get the correct value of β, such as

the Hyman method. Table -1: Illustrative Origin Destination Matrix. Here, Tij represents the number of trips from origin (O) in zone i to 2.1 Hyman Calibration Method [5] destination (D) in zone j. Oi represents the number of trips originating or the production from zone i, Dj represents The Hyman method is one of the techniques used to calibrate the number of trips terminating at zone j or the attraction the parameter in the deterrence functions. The Hyman of zone j method was found to be more robust and effective than other calibration techniques. The steps to estimate β are as The Constant Factor Method[2][4], Doubly Constrained follows. 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 ----- (5) reliance on current and past data to estimate the future when in reality the situation may not be so linear. The initial mean cost from observation is calculated as:

To the best of our knowledge, there is no Origin Destination ----- (6) study available for Kolkata. This motivates the study of the Origin Destination matrix in this paper towards modeling an The Hyman method can be described as follows: optimized public transport network for the city of Kolkata. 1. The first iteration starts by making iteration 2.1 Gravity Model [3][4] number m=0 and an initial estimate of 훽0 = 1/c*. 2. Using this value of β the new origin destination 0 matrix is calculated using the standard gravity The idea of gravity method originally came from Newton’s model. The mean trip cost c is obtained again using Universal Gravitational Law. The simplest expression of the 0 (6) and a better value of β is estimated as follows: model has the following functional form:

----- (7)

3. Make m = m+1. Using the latest value for , an origin Here, Pi and Pj are the populations of the origin and destination matrix using standard gravity model is destination, dij is the distance between origin and destination calculated again and the new mean trip cost cm-1 is respectively, and α was a proportional factor. obtained and compared with c*. If they are This gravity model was not ready to use for transportation sufficiently close, the iteration is stopped and m-1 is purpose. So, some improvements were applied including the accepted as the best estimate for this parameter; use of total trips instead of population and several other otherwise we move to step 4. parameters to calibrate the model. After the improvements, 4. The better estimate of  is obtained as: the gravity model for transportation could be used for transportation purposes. The formulation of gravity model for transportation is shown below. ----- (1) 5. Steps 3 and 4 are continued as necessary, that is, until the last mean cost c is sufficiently close to m-1 the observed value of c* . Here T is the number of trips from zone i to zone j, O is the ij i number of trips originating at zone i, Dj is the number of trips terminating at zone j, f(c ) is the deterrence function, A 3. METHODOLOGY ij i and Bj are balancing factors. cij is the cost matrix value between zone i and zone j. The value of c depends on various Data Collection: An integral part of the project was factors such as distance, speed, fare, time, comfort etc. collecting data. Given the physical limitations of live surveys we chose to use the West Bengal Public Transport ----- (2) Application [6] to obtain all the data.

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

Fig-1: The Pathadisha App to track buses.

The application is freely available in the Google Play Store or adjoining areas. We also obtained a list of 1819 stoppages iOS App Store and the end point URLs to obtain the data is which are classified as TERMINAL, JUNCTION or STOP available open source on GitHub. Using this, we obtained shown in Figure 2. Further the latitude and longitude of 1341 bus routes moving in and out of Kolkata or its close these stoppages are also available in the data.

Fig-2: A snapshot of the stoppages

Zonal Division of Kolkata: The next part included additional zones to include Dum Dum Municipal Area, dividing Kolkata into Zones to track the movement of buses. Rajarhat area and Howrah municipal Area as shown in the We considered the same ten zones from [7] along with three table 2.

Administrative Boundary Zone Region Number Borough Ward Number

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

10,11,1215,16,17,18,19, 20,21,22,23,24,25,26,27, Shyambazar, Shovabazar, Girish 2 II & IV 28,38 Park, Barabazar

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

V, VI & VII 36,37,39,40,41,42,43,44,45, BBD Bag, Sealdah, Esplanade, 4 (partial) 48,49,50,46,47,51,52,53,54, 55,60,61,62,63 Maidan

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

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

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

Golpark

74,75,76,77,78,79,80,82,83, Khidirpur, Garden Reach, Alipur, 7 IX & XV 88,133,134,135,136,137,138, 139,140,141 Chetla

81,89,91,92,93,94,95,96,97,98, Jadavpur, Tollygaunge, Baghajatin, 8 X & XI 99,100,101,102,110,111,112, 113,114 Garia

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

115,116,117,118,119,120,121, Behala Purba, Behala Paschim, 10 XIII & XIV 122,123,124,125,126,127,128, 129,130,131,132 Thakurpukur

Bidhannagar Municipality (Northern), North Dum Dum Municipality, Airport Area, North Dum Dum, 11 Madhyamgram Municipality Barrackpore, Barasat

Salt Lake, Kestopur, Bidhannagar Municipality (Southern), Newtown Kolkata 12 Hatiara,Newtown, Baguiati, Development Authority (NKDA) Rajarhat

13 Howrah Municipal Corporation Howrah District

Table-2: Division of Kolkata into Zones.

Classification of Bus Trips to Zones: Now for each terminating at places not covered in any of our 13 zones. We zone, several important stops are considered that cover the have ignored this sink vertex in our calculation of the origin entire area of the zone. So that when buses are tracked at destination matrix. This includes WBSTC buses going to each of these stoppages, all the buses moving in or out of the faraway places like Digha or Nadia. Figure 3 shows a zone is obtained without a miss. Further, since we also snapshot of the data after the bus routes have been classified obtain the vehicle numbers from the data there is no chance into zones. of counting a bus twice in a zone. For each bus route, the terminating stoppage was considered and it was classified The obtained buses at each zone were then classified as per into one of the 13 zones as above. For example, a bus Figure 3 into the zones they were going to as per Table 2. terminating or going to Sealdah will have its end zone Figure 4 shows a snapshot of the buses observed at zone 1 number as 4. A sink end zone 0 was considered for all buses and classified into end zones as per Table 2.

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

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

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

After the classification all buses available in the database calculated taking the distance between the central points of into their end zones, the next task was to obtain the buses each zone. We have already obtained the average speed as moving in a particular zone. For all the stoppages in a given 19.07 km/h. Therefore, the travel times between zones can zone i, we obtained the buses at those points in intervals of also be calculated as Time = Distance/Speed. To calculate two minutes for a duration of 20 minutes. For each zone each trip cost an assumption was taken that 90% of the from 1 to 13, the buses at that zone were obtained in a fixed buses on route are Non-AC while the rest 10% of the buses 20 minute period during peak office hours. Based on the are AC. The weighted average of the fares were taken based classification into end zones, we obtained the number of on distances. For example, the fare to travel 4 kms is ₹7 in a buses travelling from zone i to zone j as is required for non-AC bus and ₹25 in an AC bus, the weighted average of generating the origin destination matrix. We ignored the these two fares ₹8.8 is considered as fare to travel up to count of sink vertex 0 as stated previously and obtained the 4kms. Travelling in the same zone accounts for least cost of final 13 x 13 observed Origin Destination matrix as shown in ₹8.8. For others based on distance the average cost has been Figure 6. considered.

Calculation of Cost Matrix: The next part of the project The final cost matrix C is calculated as a linear equation of included calculation of the cost matrix C [4]. This cost the form: 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 Here, dij refers to the distance between zones i and j, tij refers a journey and this is normally referred to as the generalized to the time taken to travel from zone i to zone j and fij refers cost of travel. We have already obtained the speed of travel to the fare charged to travel between zone i and j. a1, a2 and of each bus and therefore we get the mean speed of travel in a3 are the weights attached to each of these figures. Since the entire city. This comes as 19.07km/h. 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 To calculate the cost function, we needed distance, travel matrix C as obtained is shown in Figure 5. time and cost of movement between zones. The distance was

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

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4. RESULTS & DISCUSSIONS minutes during peak office hours. It is to be remembered that the data was collected right before lockdown during Trip Generation: Using the data from the servers, the peak COVID-19 pandemic and therefore maybe biased. following origin destination matrix was observed in 20

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 iterative calibration technique the value of β was obtained as model was implemented using Hyman Calibration Method 0.0487 and the corresponding Origin Destination Matrix was for the above observed trip matrix in Figure 6. From the obtained as shown in Figure 7.

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

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Discussions: The study estimated the number of bus trips removal of redundant routes and allocating new routes. in the morning for the region of greater Kolkata. The demand Beyond public transport, private vehicles also have to be matrix is obtained as shown in Fig-7 from the supply matrix considered for estimations. Urban planning of cities have to as shown in Fig-6.The total demand deviation calculated as be based on these methodologies. difference between observed ƩijTij from the estimated ƩijTij is obtained as 6.57%. However, considering only zone 1-10 as REFERENCES the Origin Destination Matrix this deviation would have been reduced to 2.82%. This difference can be probably attributed [1] Wikipedia: Transportaion Forecasting. Retrieved: June, to the biased data obtained due to lockdown for zone 11, 12 2021. https://bit.ly/3vaCz9Z and 13. Trip Distribution was also implemented by methods [2] Salter R.J. 1989 Trip distribution. In: Highway Traffic other than Hyman Method. The total demand deviation was Analysis and Design. Palgrave, London. Springer obtained as 11.41% and 23.09% for these ineffiecient power [3] I Ekowicaksono, F Bukhari and A Aman 2016 IOP models. More such estimations could have been done at Conference Series: Earth and Environmental Science several time intervals of the day to obtain better results. Volume 31. Estimating Origin-Destination Matrix of Bogor City Using Gravity Model Further, if we look at the productions (Oi) and the [4] Trip distribution Chapter 8, NPTEL Published: May, attractions (Dj) the values are close to the observed values 2007. Retrieved: June, 2021. https://bit.ly/3glol0x for most zones except Zone 4. Zone 4 consists of Central [5] G M Hyman 1969. The Calibration of Trip Distribution Kolkata where the mobility is very high and therefore the Models. London Environment and Planning pp 105-112 demand for buses originating or terminating is also high in [6] Pathadisha App on Google Play. https://bit.ly/2TMBibU 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 [7] Tuhin Subhra Maparu and Debapratim Pandit 2010. Institute of Town Planners, India Journal. A to be remembered that the data was collected during the Methodology for Selection of Bus Rapid Transit pandemic and therefore the data may not fully account for Corridors: A Case Study of Kolkata the situation in normal days. But the methodology used will [8] Wikipedia: Trip Distribution. Retrieved: June, 2021. be the same. The calibration parameter as obtained from the https://bit.ly/35qQqhN 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 © 2021, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 2225