3. 4. 5. 6. Demand. Figure 2: Route Breaking. New routes [1, 2, 3], [4, 5] and [5, 6] ..... Louis Berger International Inc, East Orange, New Jersey, USA, Sri Lanka ...
DEVELOPMENT OF A METHODOLOGY FOR BUS ROUTE NETWORK PLAN FOR THE WESTERN PROVINCE R.M.N.T. Sirisoma, J.M.S.J. Bandara and Amal Kumarage Department of Civil Engineering, University of Moratuwa ABSTRACT Effective design of transit routes and service frequencies can reduce the overall cost of providing transit services, which generally consists of user costs and operator costs. Both these parties will prefer to minimize their own costs. The route design problem is very complicated due to its multi-objective nature, the non-linearity and non-convexity of the objective function that represents the cost function. Therefore, a number of computer algorithms are to be used to develop a methodology for designing the route network for the Western Province. Initially only the demand and travel distance will be taken into account and at a later stage, this network can be modified to minimize the number of transfers made within the system. The main objective of this research is to find an acceptable network that minimizes total cost including invehicle and transfer cost of bus passengers. A separate algorithm is to be used to generate the route network so that all nodes in a network have to be served at least by one route. In this algorithm, while constructing the route, it will consider the O-D pair with the maximum demand in the network demand matrix. It will then assign that demand along the minimum path route between those two nodes assuming all the passengers would select the travel path with the shortest distance. Then the program checks for the second highest demand pair and assigns that demand along the shortest path between those two nodes. Likewise all the demand values can be assigned to the network along respective minimum paths. After generating the routes based on the passenger demand along the minimum path rule, the user of the program has the choice to modify the network using set of algorithms for route breaking, route merging, changing the crossover points etc. in order to minimize the transfer trips in the entire system. This would be an iterative process until the user is satisfied with the designed route network. A methodology for route design for any transit system is presented in this paper.
INTRODUCTION Effective design of transit routes and service frequencies can decrease the overall cost of providing transit services, which generally consists of passenger costs and operator costs. Both the operator and the user will prefer to minimize their own costs. The user costs includes the entire in-vehicle time and transfer time. The route design problem is complicated due to its multi-objective nature and the non-linearity and non-convexity of the objective function (Ofyar at al 1993). Non-availability of passenger demand data is another constraint. Therefore, the calculated demand O-D matrix can be used to identify the passenger demand distribution over the study area. Other than that the road inventory details such as nodes, links, neighbouring nodes, link length and bus terminal points should be available. In this research, only the routes, which operate in main corridors between Divisional Secretariat Divisions, will be considered. There are several types of routes such as ring routes, feeder routes, line haul routes etc. Nevertheless, not all these route types can be analysed together. One reason is smaller routes would not be available
at the planning stage. Other reason is demand for feeder and other local routes will depend on the arrangement of main route network.
From the passengers point of view they would always like to have their trips with in a minimum travel time and a minimum cost. But operators would prefer the maximum profit with a higher demand level. Therefore, the final solution should be justifiable for both parties and the main objective of this study is to find a solution that minimises the in-vehicle travel time and the transfer time of the passengers of the whole network (Markwah at al 1997). Here, it is assumed that the passengers prefer to use the minimum travel time path to their destinations. In order to minimize the total cost of passengers travelling from their origin to destination, the following objective function can be used. Minimize Travel time cost, which is given by
C t × D ij × IVTTij Where Ct– Cost per unit time per passenger Dij – Demand between node i and j IVTTij – In vehicle travel time between i and j Optimum Route Network Beginning with any node the first stage involves choosing the shortest possible link to another node. The second stage involves identifying the unconnected node that is closest to either of these connected nodes and then adding the corresponding link to the network. This process would be repeated until all the nodes have been connected. The resulting network is called as the optimal route network. Assumptions The following assumptions have been used in the algorithm to determine the optimum route network. 1. The demand pattern (i.e. O-D table) is static and remains constant for all periods of study. 2. A passenger will choose the route to their destination based on the shortest travel time. 3. Every bus in the system travels with constant speed on all parts or links along the route. 4. Travel demand is symmetric in the system (i.e. the O-D matrix is square and symmetric). 5. Routes can have partial overlaps. 6. All buses have the same capacity. 7. All buses are in good condition and operate for all 30 days per month.
Route Generation The first step of this process is to generate routes in the existing route network. According to the demand, routes should be introduced for every link in the system. A separate algorithm should be used to generate the route network with the constraint that all nodes have to be served by at least one bus route. For the construction of the route network, the maximum demand O-D pair from the demand matrix is considered first. Then it will assign that passenger demand along the minimum path route assuming all the passengers travel along the minimum path. Then it will check for the second highest demand pair and assign that demand along the minimum path between those two nodes. Likewise all the demand values can be assigned to the network along minimum paths. All the demands between nodes along this route should be added to that route so that it can be added some overlapping routes to the assigned route. Route Merging When several routes terminate at one node and if there are several possible ways to join two routes 1 and 2, the route merging can be carried out. Two separate routes having the same terminal can be added together so that it will serve a direct route for the passengers minimizing their transfers. The first route can be selected randomly and the second route should be selected so that it saves the highest number of transfers from that common node (Figure 1). When adding the routes the decision can be taken on the basis of demand density (demand per unit distance), because merging may be not cost effective for a lower passenger demand 4
20
4 R1/45
R3 15 1
1
R1
10
2
2
5 R2
20
R2/25
10
3 3
Figure 1: Route Merging Route Breaking This route breaking can be done for routes exhibiting a significant variation in demand over their length. On each route the demand difference between each link can be recorded. The route which has the highest difference can be split into different routes (refer the figure below). The link with the least flow will become a route by itself.
Because of its low flow, it can operate with higher headways with a lesser number of buses. If the link with the least demand happens to fall at the end of the original route, only two routes would be generated. (Figure 2) Demand
Demand Difference
1
2
3
4
5
6
Figure 2: Route Breaking New routes [1, 2, 3], [4, 5] and [5, 6] Alternately, it can be spilt into two different routes if the transfer demand is very high. Then the operator will be able to cover his operating cost from the available demand. Route Sprouting (Overlapping Routes) In this algorithm, the decisions can be made to introduce overlapping routes to the system. If the demand on certain links are relatively high compared to the other links one bus route may not be enough to serve the demand. Therefore overlapping route can be introduced in those links with a smaller fleet size. Here the procedure is opposite of the route breaking. It should be identified the highest difference in the link flows along a route and it can be called as the critical demand link. The critical link can become a separate route and this demand can be served by overlapping routes. (Figure 3) Demand
Critical Demand Difference
1
New Routes
2
3
4
5
Figure 3: Route Sprouting [1,2,3,4,5] and [3,4]
Identify the Route Crossover Points Crossover can be explained by the following example.(Figure 4) 9
7
R3
R2
R1
R1 1
2
R1
R1 3
4
5 R3
R2
8
6
Figure 4: Route crossover points If route R1 intersects two other routes R2 and R3 the intersection point can be selected to break that route into two routes. For this figure, the possible crossovers are as follows.
Name Original Crossover 1 Crossover 2 Crossover 3 Crossover 4
Route R1 [1,2,3,4,5] [1,2,6] [1,2,7] [1,2,3,4,5,9] [1,2,3,4,5,8]
Route R2 [6,2,7] [7,2,3,4,5] [6,2,3,4,5] [6,2,7] [6,2,7]
Route R3 [8,5,9] [8,5,9] [8,5,9] [8,5] [9,5]
The purpose of doing this is recombining two routes to minimize the number of transfers and reduce underutilization of the buses along certain locations. For every intersection between two routes, there are four possible routes that might come up in the existing solution (Figure 5).
9
7 3
1
5
1
2
3
4
5
6
4
2
7
8 8
6
Figure 5: Possible routes at an intersection The selection of new route will depend on the savings of transfer demand, which is sum of the all O-D flows along that route completely. For example selection 3 would consists of O-D flows [7,3], [7,4] and [7,5]. Analysis of Sample Route Network Using above algorithms and demand O-D matrix, a route network can be designed. Let us consider a sample O-D matrix as in the table 1, which shows the average demand per hour and the existing road network with the distances between each node (Figure 6). Thereafter, this demand should be assigned to the route network. If we consider the minimum path as the design criteria it will not give any picture on the origin of the trip, the transfer nodes and number of transfers per trip etc. Therefore, when we design the network it is necessary to consider the demand, origin destination and transfer points. Therefore, the passenger assignment and the route generation should be done in parallel to each other. At the same time, the transfers at each node and the path of the trip should be tabulated. Node 1 2 3 4 5 6 7 8 9 10 11 Total
1 5 2 1 8 6 2 5 4 3 2 1 39
2 2 4 1 10 12 5 2 1 6 7 1 51
3 1 1 8 2 10 4 8 9 3 1 2 49
4 8 10 2 6 3 4 2 9 12 6 2 64
5 6 12 10 3 8 10 15 6 4 2 1 77
6 2 5 4 4 10 3 2 4 8 7 5 54
7 5 2 8 2 15 2 8 6 3 1 2 54
8 4 1 9 9 6 4 6 10 8 4 5 66
9 3 6 3 12 4 8 3 8 2 6 8 63
10 2 7 1 6 2 7 1 4 6 9 3 48
Table 1: Sample O-D Matrix
11 1 1 2 2 1 5 2 5 8 3 6 36
Total 39 51 49 64 77 54 54 66 63 48 36 601
• • •
According to the O-D matrix given in Table 1, the highest demand is from node 7 to node 5. Therefore assign that total demand in route 1 (R1). The second highest demand is from node 5 to node 2. That should be assigned in the minimum path i.e. 5-6-2. The passengers from 5-6 and 6-2 should be assigned to the same route (R2). Similarly, the whole demand should be assigned and if there are no direct route transfer nodes are tabulated as in the Table 2. The Figure 7 shows the assigned demands is shown in circles and route number is also given.
Origin Node
Destination Node
Transfer Node 1
Transfer Demand
Route Before Transfer
Route After Transfer
4
1
6
8
R4
R7
4
2
6
10
R4
R2
8
3
5
9
R6
R5
8
4
5
9
R6
R5
9
6
4
8
R3
R4
9
11
4
8
R3
R10
9
2
4
6
R3
R4
5
1
6
6
R2
R7
10
2
4
7
R12
R4
10
6
4
7
R12
R4
11
6
4
6
R10
R4
11
8
4
5
R10
R5
8
1
7
4
R11
R14
8
6
5
4
R6
R2
9
5
8
4
R8
R6
10
8
4
4
R12
9
1
4
3
R3
9
3
4
3
R3
R5
9
7
8
3
R8
R11
7
2
1
2
R14
R16
7
4
5
2
R1
R5
10
1
4
2
R12
R4
10
5
4
2
R12
R5
11
7
4
2
R10
R5
3
1
2
2
R16
R18
8
2
5
1
R6
R2
10
3
4
1
R12
R5
10
7
4
1
R12
11
1
3
1
R17
11
2
3
1
R17
R18
11
5
4
1
R10
R5
Total Transfers
Transfer Node 2
Transfer Demand
Route Before Transfer
Route After Transfer
6
9
R2
R9
6
6
R4
R2
6
7
R4
R2
5
5
R5
R6
R5
5
4
R5
R6
R4
6
3
R4
R7
6
2
R4
R7
5
2
R1
R5
R5
5
1
R1
R5
R18
2
1
R18
R16
132
Table 2: Number of transfers
40
4
9
2
1 3
3 13 6 10
5
6 6 5 12
4
11
8
7
8
12
5 5
12
6 6 6
3
10
9
14
8 14
* The link distances are shown in the cages Figure 6: Existing Road Network with the Link Distances 6
R18
2
R16
4
1 36 3
10 R2
19
4
R9
13
R7 25
R17
6 R5
65
R14
R4
R9 38
10
4
11 23
R10
7 R2 R5
20 R1
3 30
52 5 32
R11 42
R15
R12
R3
10
15 R6 9 8
15
R13 6
R8
Figure 7: Assigned Demands in each Route
To minimize the number of transfer trips the above network can be used. Now we can use the algorithms of route merging, route sprouting, route breaking etc. to change the route terminals. All the possibilities of merging routes can be checked and decision of adding routes, breaking routes or introducing overlapping routes can be taken with the help of route density. If the demand is less, a short distance route may be profitable with a small fleet that operates in a lower headway. To check for route sprouting the demand variation along the route is plotted. If there is a critical demand or higher demand variation, an overlapping route is introduced and the transfer saving is checked. For example consider the demand variation from node 8 to node 3 (Figure 8) Demand
52
Critical Demand Difference
42
25
8
5
4
3
Figure 8: Demand Variation between Node 8 and Node 3 Considering the demand variation an overlapping route can be introduced from node 8 to node 4 so that it will save 17 number of transfer trips in the system. Similarly, all the route can be checked for route sprouting. For this system, it does not need to change the crossover points since most of the transfers take place from either node 6 or node 4 and 53 transfer trips can be saved in route merging. The final route network and the demand densities are given in the figure 9 and table 3
6
R16
2
R16
4
1 36 3
10 R2
19 13
4
R9
R7
25
R17
6
R11
R5
65 R4
R9
R3 38
10
4
11 23
R10
7 R2
R6
20 R1
R5
3 30
52 5 32
R11 R6
R3
42 10
15
R5 9 8
R13 6
R8
15
Figure 9: Final Route Network
Rote R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R13 R15 R16 R17
R15
R4
Link 7-5 5-6-2 9-4-6 10-4-6 8-5-4-3 8-5-4 1-6 8-9 7-6 4-11 8-7-1 9-10 10-11 1-2-3 3-11
Demand 20 74 49 78 92 27 19 15 10 23 28 6 3 10 4
Distance 5 11 11 11 21 15 6 14 12 8 16 14 12 15 5
Density 4 7 4 7 4 2 3 1 1 3 2 0 0 1 1
Table 3 : Demand Density in Each Route
CONCLUSION The algorithm developed in this paper, can be used to design a bus route network for the Western Province. In the first stage, it can develop a bus route network considering the demand values in the O-D matrix. Then the user of the algorithm has the authority to change the network using the sub-algorithms of route merging, breaking, sprouting etc. The main objective function used in this process is to minimize the number of passenger transfers made within the defined network. In addition, the user can attempt to optimise the operator costs, since each route and each node will improve the service to the passengers but will increase the operators cost. Therefore, there should be a compromise between these two states. The proposed program can be used for other geographic areas if the relevant network and demand data and socio economic data is available for that particular area. At the same time, the user of the program should be knowledgeable on the existing route network and the road details, since the final solution needs to be based on human judgement as well as artificial intelligence. REFERENCES 1. Ana I. Ramirez and Priyanka N. Senevirathna, Transit Routine Design Applications Using Geographic Information System, Transportation Research Record 1557 2. Bandara J.M.S.J., Weerasinghe S.C. , Gurofsky D. and Chan P., Grade Separated Pedestrian Circulation Systems, Transportation Research Record 1438, page 59 to 66 3. Kumarage et al, Department of National Planning, Ministry of Finance and Planning, Colombo, Sri Lanka, Assessing Public Investment in the Transport Sector, September 2001 4. Louis Berger International Inc, East Orange, New Jersey, USA, Sri Lanka Transport Sector Planning Study Final Report – Buses, Volume 3, Resources Development Consultants Ltd., Colombo, Sri Lanka 5. Mahmood Omar Imam, Optimal Design of Public Bus Service with Demand Equilibrium, Journal of Transportation Engineering, September-October,1998 6. Marwah B.R., Farokh S. Umrigar and Patnaik S.B., Optimal Design of Bus Routes and Friquencies for Ahmedabad, Transportarion Research Record 994,1997 7. Ofyar Z. Tamin, Public Transport Demand Estimation by Calibrating a Trip Distribution- Mode Choice (TDMC) Model From Passenger Counts: A Case Study in Bandung, Indonesia, Journal of Advanced Transportation, vol 31, 1993 8. Srinivas S Pulagurtha and Shashi S Nambisan, Estimating Time Dependant O-D Trip Tables During Peak Periods, Journal of Advanced Transportation, Year 2000, Vol. 34, No. 3 9. Wijesundara W.W.M.R.K., Development and Testing of a Set of Mathematical Models for Travel Demand Estimation, Report to Partially Fulfillment of the Requirement of the Degree of Master of Engineering, Department of Civil Engineering, University of Moratuwa – Sri Lanka, June 2001 10. Wong S.C and Tang C.O., Estimation of Time Dependent Origin Destination Matrices for Transit Networks, Transplan Res-B, Year 1998, Vol. 32, No. 1,
