A New Public Transport Assignment Model *

Transcription

1 A New Public Transport Assignment Model * B. Horváth Széchenyi University Department of Transport H-9026 GYŐR, Egyetem tér 1. hbalazs@sze.hu Abstract: In my article I reviewed the past achievements of the topic and the theoretical methods together with the practical models. After the assessment analysis of these models I built up my new approach assignment model. The detailed description of the model is complete with the presentation of an experiment done on a real public transport network. Keywords: public transport, simulation, assignment, transport planning 1. Introduction Our objects are the solution and the balancing between the advantage and the harmful effects of transport. Other words how can we solve the growing mobility demand take into account the sustainable development can be read on the homepage of the Ministry of Economy and Transport. It is clear only from this sentence that the problems of transport can be solved only with long term plans. To consider this idea is born the Hungarian Transport Policy which hold up the development of public transport among the main priorities: - In the passenger transport, preference of the public transport against the private transport, promotion of the bicycle traffic, increasing of the safety and convenience of the pedestrian traffic. Beyond these the public transport stand appraised among the emphasized short terms priorities of the Hungarian Transport Policy: - Providing a modern and high quality local and interurban public passenger transport, as a first step, implementation of a new common prepaid cart system providing access to all transport companies in Budapest and its attraction zone (Budapest Transport Association). These Hungarian objects hang together with the European Transport Policy where the better utilization of the present public transport systems appears on the one hand: * This article is the summary of the PhD thesis: Balázs Horváth: Assessment analysis and development of public transport assignment models; Budapest University of Technology and Economics

2 In response to the general deterioration in the quality of life of European citizens suffering from growing congestion in towns and cities, in line with the subsidiary principle the Commission proposes to place the emphasis on exchanges of good practice aiming at making better use of public transport and existing infrastructure. On the other hand the object is to improve the competitiveness of the public transport: We therefore need to make the alternatives to the car more attractive in terms of both infrastructure (metro lines trams cycle tracks priority lanes for public transport) and service (quality of service, information given to users). Public transport needs to achieve levels of comfort, quality and speed that come up to people s expectations. From all these is outlined that already the Hungarian and the European Transport policy take care public transport and calculate upon it as one of the best solutions to solve the problems of urban transport. As part of these solutions it is important to have an optimal modal-split. Public transport has against private transport among others following advantages: - Less specific environmental pollution o Air pollution o Noise pollution - Less specific space request o On the road o Parking lot - More transport safety - Less specific energy consumption Because of all these it is important to have a well working public transport system which is suitable to the applied transport policy. To plan such a high quality public transport system needs accuracy and reliable forecasting tools. The key of a public transport planning model as well as in general the key of the planning of a public transport system is the correct forecasting of the probable number of passengers. It means the correct calculation of the planning step assignment. Because of these I will focus only on the public transport assignment models. I worked out a brand new public transport assignment model together with a new matrix conversion method which I will introduce at the end of my article. 2. Main steps of the transport planning The traditional transport planning included four steps [9]: - trip generation - trip distribution - mode choice - assignment In the first three steps it can be detailed the transport demand, while in the fourth step it can be compare the demand and the supply side of the transportation system. 94

3 2.1. Trip generation The aim of the trip generation is to define the origin and the destination traffic of each zone. It can be sign as P i or A j. The result of this step is the number of the origin and destination trips in each zone, practical the sum of the rows and the columns in the OD matrix (OD matrix means the origin-destination matrix). [12] The main methods in the trip generation divide the trips into three major groups: - trip motivation - trip timing - trip maker The trip motivation models divide the trips into two groups home based and non home based. Most of the trips are home based, so they can be divided into further groups like: work, school, shopping, leisure, others. By trip timing it can be peak or off peak trip. Most of the trips are peak hour trip. Trip maker can be important because of income level of car ownership or general standard of living. The trip generation models can be divided into three groups: - growth rate models [2] - regression models [9] - category analysis The main ideas of all models are, that the traffic of the future can be deduced either form the present traffic or from the forecasted data of the area (inhabitants, workplaces ) Trip distribution The aim of the trip distribution is to calculate a destination to a given origin or to calculate an origin to a given destination. It means practical filling of the matrix interior. [12] There are lot of models to calculate the trip distribution. All of them have to fulfil three rules: - forecasted number of trips from a given origin zone have to equal to the forecasted number of origin trips in this zone - forecasted number of trips to a given destination zone have to equal to the forecasted number of destination trips to this zone - forecasted number of origin and destination trips for the whole area have to be equal 95

4 i j i P f f i i, j i (1) i, j j P A The two major groups of distribution models are: - growth rate models (e.g.: Fratar, Detroit model) - synthetised models (e.g.: gravity model) The common idea behind the models is: The number of trips betweens two zones: - grow if the attractiveness of these zones for a given group of trips is grow - fall if the resistance against the trip is grow In the last times there are even newer models developed based on the entropy-theory Mode-choice A j j The aim of the mode choice is to determine the used mode for a given trip. Usually there are two modes: public transport and individual transport. Sometimes there are models for several modes, they are the multimodal models. Other way to calculate the mode-choice is the direct demand model, which included all three steps of transport planning (generation-distribution-mode choice). The result of the mode-choice is several matrices which are generated from the matrix resulted in the trip distribution. Although trip distribution and mode-choice can be transpose each other, because there is a close relationship between these two steps. The mode-choice is not only question of thinking but fashion or personality. Therefore it is not a simple mathematical problem. The three major factors to choose a mode are [12]: - trip maker (car ownership, income rate, place of living, family-children) - trip (motivation, timing, length) - transportation system (quantity: time of the trip, fare level for trip or parking, quality: comfort, safety, accuracy) There are two major groups of mode-choice models: - aggregated models - disaggregated models At the aggregated models the basis are the zones, while at the disaggregated models the base are the trip makers. One of the most common used models is the Logit type models [8]. 96

5 2.4. Assignment As long as in the first three steps goes on the detailing of the demand in this fourth and last step of the transport planning goes on how can supply solve the demand. The aim of the assignment is to calculate the traffic of each element of the system (like roads, junctions, busses ) and other relevant numbers characterising the network [12]. The assignment methods are developed from one origin into several different directions. All of the models need three groups of information to calculate the needed data: - demand, OD matrices - traffic network (system) - route choice preferences Majority of the methods have a similar working structure, which included two steps: network building, route-choice. In the first step the models build up a mathematical structure for the transportation system, in the second step the methods are searching an optimal route between two given zones. Optimal route can be the shortest, the quickest, the cheapest it depends on the preferences. Usually this optimal route is called as the shortest path. By the method we can group the models like follow [14]. One step Multi step One route All or nothing Simply capacity restraint Multi route Simply multi route Capacity restraint Table 1 Basic model in assignment One route one step: These are the simplest models. The traffic goes in all cases through the basically shortest path. All the other routes remain empty. Multi route one step: Similar to the previous models the shortest routes are unchangeable, but a given route can have only a part of a given load, it means the traffic between an origin and a destination can be shared among several routes if they have similar length. Naturally the shortest route will get the highest load, the second shortest the second highest and so on. One route multi step: These and generally the multi step models are the capacity restraint models. The main point of this method is that the traffic is loaded to the network on several steps. After each step the length of the routes are calculated newly subject to the previously calculated loads. Therefore the structure of the shortest routes can be change time after time. So the overloaded routes will be out of calculation. This way it is possible to show the effect of congestions. Multi route multi step: These models are the most complex ones among the assignment models, therefore these are the methods which are able to map the real life most accuracy. The models are working in several steps and in each steps there are several possible routes. The base of these kinds of models is that the volume-delay function has to be minimal. The volume-delay function is like follows: n vi F( v) s ( v) dv (2) i 1 0 i 97

6 where: F(v) volume-delay function (the sum of the system costs) v i load on the route i. s i (v i ) impedance of route i at load v i n number of routes The objective function is than: F( v) minimal, other way ' ( F ( v)) 0 (3) Generally this objective can be solved only in several step, therefore these methods are iterative style models. The problem is that not all the travellers are able to follow the theoretical shortest path, therefore there are a coincidence factor which can be influence the route-choice, and so the loads. To solve this problem there are stochastic models which can take into account these factors. 3. Public transport assignment models Basically there were only models for assignment of road traffic, but no models for public transport networks [12]. Later there were models from road traffic assignment deduced for public transport assignment. These models were not good enough to give a detailed view about a given public transport network. Although majority the common used models are working on the same basis they are much better, but can be use under strict limitation, other way the results can be wrong. These models can be used, if the public transport network fulfils the following requirements: - public transport is mass transport (numerous lines, numerous passengers) - high frequency (small head time subject to the travel time) - lot of direct lines, small amount of transfers - steady coming of passengers into the stops If these requirements not fulfilled, or only partly, the common assignment models cannot be used. That is why there is a need for more accuracy public transport assignment models. The development of the public transport assignment models has not a long history. The first models are coming from the late sixties, but the early models could not explore the mathematical background of the public transport assignment models. It happens only in the last years. After all there were important milestones in the early times like the models of Dial, Le Clerq [5], Chriqui [4], Chapleau, Andreasson, Rapp et al.. Others combined the assignment with the network planning like Lampkin and Saalmans, Schéele, Mandl, Hasselström. From these models only Florian later Florian and Spiess used multimodal methods. These models have not capacity restraint although De Cea pointed only capacity restraint models are able to model the traffic flow on a loaded public transport network. 98

7 Accordingly common public transport assignment models can be grouped basically into two major groups: - capacity restraint - without capacity restraint Capacity restraint models are coming later, like Spiess, later Spiess and Florian [15], De Cea, De Cea and Fernandez, Le Clercq [5], Chriqui [4]. Later there where even accuracy models from Gendreau, De Cea and Fernandez [7]. While Abdulaal and LeBlanc used a mathematical approach. Spiess and Florian developed its own model further and had finally a reliable model for the assignment, although it was not free from the common failures of the traditional assignment models. Lastly Mahmassani [1] did a dynamic assignment model, which can be a transition from traditional to new stream models. In the last then years there are new streams in the developing of the assignment models. It is leaded by Nuzzolo, Russo [10], Crisalli [6] and Hickman. The methods of this new stream called schedule based assignment models [3]. After these there are two groups of assignment models: - frequency based (common or traditional models) - schedule based The main differences between these two groups can be summarised in three points [11]: - frequency based o line based o average head times o results: average loads - schedule based o run based o timetable based head times o results: accuracy loads for each run This new kind of assignment models give an even precise picture about the network, but need a lot more information for accuracy results and sometimes have the same problem as the traditional models. 4. Failures of the common public transport assignment models The main faults of the public transport assignment models are focused on the following four fields: - Conformity between passenger demand and transport system (supply) - Question of transfers - Handling of capacity restraint - General failure 99

8 The used public transport assignment models solve the conformity between passenger demand and transport supply barely. While a public transport system can be reach both time and space limited the analysis of a public transport system should be explore not only the route of an origin-destination trip but the time of the trip and the used run of a line. Both the frequency based and the most of the timetable based assignment methods use average passenger number. It means there is a comparison between average demand and average supply. This approach has serious failure because of the written limitation in reach of the system. The numbers of passengers are varying from run to run therefore to use average numbers gives wrong results. Most of the used public transport assignment models handle the question of transfers wrong. The common frequency based assignment models use average passenger numbers similar to the origin points at the transfer stops. These numbers are based on the frequency of the single lines. This calculation using average numbers can give wrong results. That is why frequency based methods can not follow the aligned timetables. It is true that with the help of some parameters the given results will be good enough to use it for the planning work on a solid level. Most of the used public transport assignment models can not handle correct the capacity restraints of a public transport system. The capacity restraint frequency based public transport assignment models can characterize the capacity of a public transport vehicle only with some resistance function or uncomfortable function maybe with modification of the waiting time at the origin stop. This approach can not be accept if the frequency on the network is low or the public transport system works on its capacity restraint or near to it. This problem looks very similar to the question of the dynamic demand- dynamic supply but point further. To solve the problem of the capacity restraint it is not enough to simulate the public transport system on the level of runs, it is important to model also the demand on personal level passenger by passenger. The use of a common public transport assignment model can not image the process running on the public transport system. The aim of the analysed models is to calculate the numerical results of the planning step assignment. They can show only the numbers about the studied public transport system. Therefore they are not able to show the processes running on the public transport system. Hence of this these models are only able to control a given public transport system. With this control we can only rate a given plan. To solve this last problem I introduced the concept of the result-based and the processbased assignment model groups. It is necessary while the aim of the analysed models is to calculate the numerical results of the planning step assignment and therefore they can show only the numbers about the studied public transport system. Therefore they are not able to show the processes running on the public transport system. Hence of this these models are only able to control a given public transport system. With this control we can only rate a given plan. If the models could image not only the 100

9 numerical results but the process running on the public transport system, it could be help to: - Explore the failures in the public transport system - Give new planning ideas, new alternatives I divided the public transport assignment models into two groups: - result-based - process-based models. The nowadays used assignment models belong to the group of the result-based group because they aim is only to produce numerical results about the studied public transport system. A model can be process-based if it can produce the common results but as surplus can show the traffic processes on the public transport system. It means that these models allow to follow the work of the public transport system in time and space to fulfil the objects (explore the failures in the public transport system; give new planning ideas, new alternatives). Process-based analysis is possible by using simulation based assignment methods. The use such a method makes possible to have results similar to the common numerical results but more detailed and more accuracy other way it makes possible to follow the processes on the public transport network. 5. A new public transport assignment model I worked out a new public transport assignment model. This suggested new method is a process-based timetable-based capacity restraint simulation-based public transport assignment model. The main point of the method is that all the passengers and all the vehicles are discrete elements of the model. The method plays back the processes running on the public transport system similar to the real life. This kind of simulation of real life looks not resource effective but can describe the real process with high accuracy. 101

10 Input data Steps of the assignment method Output data (Results) Passenger demand - O-D matrix(s) Generation of passenger demand Network model - Stops - Lines - Timetable Route-choice criterions Dwelling at a stop Vehicle movements Route-choice Simulation process Simulation process - Events on the network Results of the assignment - Passenger numbers - Occupancies 102 Figure 1. Working process of the new suggested public transport assignment model The big difference to the common models is that at this model not only the numerical results but the process itself is important. It is possible to follow all the processes running on the public transport system like a movie. At this model can be follow the passenger flow at a given stop, or the functionally or disorder of a transfer point. The method has two main parts: - Generation of passenger demand - Dynamic route-choice The model is working like shown at figure 1. The main point of the work of the model is that the two main parts are working separate but not independently, they have a time phasing. The correct work of such a model needs dynamic information about the passenger demand and about the public transport system. This dynamic approach brings on three major problems: - representation of the demand side - handle the connection between desired departure time trips and timing of the public transport system - representation of the supply side (public transport network) To solve this second problem between desired departure time trips and timing of the public transport system I worked out a matrix conversion method which is able to handle this close connection between desired departure time trips and timing of the public transport system. What is this problem actually? In the morning peak time most of the trips are desired departure time trips (DDT trips) which has a close connection to the timing of the public transport system. Therefore the O-D matrix has also a close connection to the timing of the public transport system. If we want to show accuracy passenger demand we need to describe this close connection between desired departure

11 time trips and timing of the public transport system. The common O-D matrices are not able to describe it. To describe this close connection means to correct the O-D matrices to have the needed information. It follows that a present O-D matrix is not able to analyse new, planned public transport system. Therefore it is needed to correct the present O-D matrix to be able to analyse a new, planned public transport system. To do this I worked out a matrix conversion method. The matrix conversion method has two steps. Through the first step we convert the observed passenger demand which is stored in the observed O-D matrix to real passenger demand. In the second step we convert this real passenger demand considered the planned public transport system to appeared passenger demand which will load the planned public transport system. In the first step of the method we turn an observed trip with T A departure to a real trip with T B arrival time: T B TA tel, m (4) where: t el, m is the journey time at the time point of the passenger count In the second step this theoretical arrival time T B will be transferred to T A theoretical departure time: T ' A T t (5) B ' el, m where: t el, m is the journey time at the time point of the analysis With this new T A we will have a more accuracy picture about the passenger demand, with which we can do a more reliable assessment about a public transport system. Considering to the mentioned first and third problems (representation of the demand and supply side) I worked out a new representation of the demand and supply side of a public transport system. As written the dynamic representation of a public transport system requires that both passenger demand and public transport system (supply) will be dynamic represented. 103

12 User group 1 C 1 1 C 1 2 C 1 3 C 1 k User group 2.. User group n C 2 1 C 2 2 C n 1 C n 2 Figure 2. In time vary (dynamic) matrix representation I developed a new matrix representation which is able to show the dynamics of the passenger demands. One of the base requirements of the new assignment model is to have an accuracy dynamic O-D matrix. I worked out a matrix representation which can show the passenger demands in time and on the level of the different users. This representation is several chains of O-D matrices. There is a main chain in which there is a general passenger demand appears on the public transport network. The temporary passenger demands of a given special user group will stored in another chain which is parallel to the main chain. There is the possibility to have a second or a third complementary matrix chain. Such a special user group can be the pupils the students or the industrial shift workers. It is not necessary to be continual this complementary matrix chains. Only the main chain should be continual through the whole day. 104

13 time T (time) S 4 S 2 S 5 S 1 S 3 C (x 1, y 1, t 1 ) E Vehicle movement or dwelling F Attendance of passengers at a stop L space 1 B stop s stop s A space X (space) Y (space) L 2 K (x 0, y 0, t 0 ) Figure 3. Public transport representation in time and space The public transport system, as the supply side will be represented in a three dimension (x,y,t) space defined graph. The public transport system (network and the line system with timetable) is represented in a time-space system. In this representation each stop with an x,y coordinates are permanent time axles at the given x,y point. The runs of the lines are links in time and space between these time axles representing the stops. The start of a passenger s trip will therefore begin at a given t 0 point on the time axle of the origin stop. The end of a trip will be a t point at the time axle of the destination stop. After these the shortest path search can be described as follow: We are looking for a route U on the graph G defined in time and space from a given point represented with x 0, y 0, t 0 to a given time axle represented with x 1, y 1. Aim of the route search is to have a route which t 1 at x 1, y 1 is the least. A possible route on this time-space system shows figure 4. Figure 4. A possible route on the time-space graph 105

14 6. Real network test of the new model I have made an experiment with the finished model. I tested it on a real public transport network. I used to this experiment the public transport network of the city Győr from the year 1997 [13]. Through the experiment I compared the results of the model with the results of a control system (VISUM) and with the results of the passenger count. This real network test is running on a network with 393 stop points, what means 215 different stops. The length of the network is 115,3 km, on this network there are 47 lines with 99 vehicles. The average daily passenger number is 143 thousand passengers. The network system is mainly radial with few diametrically running lines. There is a big transfer point in the Downtown. The test is running on an average workday. I have three data: - traffic count - VISUM transport planning system - new assignment method As summary of the test there are the main important parameters: Parameters Visum New method Traffic Value Deviation Value Deviation count Average travel time [min] 14:05 4:19 23,46% 15:23 3:01 16,39% 18:24 Average ride 12:51-2:09 20,09% 13:12-2:30-23,36% 10:42 time [min] Average travel 4,451-1,351-43,58% 3,92-0,82-26,45% 3,1 distance [km] Average travel speed [km/h] 20,8-0,9-4,52% 17,8 2,1 10,55% 19,9 Sum passkilometre ,99% ,54% [passkm] Passengers ,76% ,76% [Pers] Number of ,32% ,25% boarding [Pers] Transfers [Pers] Without ,39% ,73% transfer 1 transfer ,13% ,77% transfer >2 transfer Table 2 Results of the real network test The results showed that the new model is good enough to use in practice. It produced 8 better results out of 10 against the control system. 106

15 Conclusions The new model can be use on three major fields: - Analysis of probable effects of a public transport development - Support of the aims of the transport policy - Education With the help of the new model it is possible to analyse probable effects of a public transport development or estimate the difference between several development plans. This model is a new more accuracy tool to help the decision makers to return the optimal verdict. My method can support the realization of the aims of the transport policy like preferring public transport or develop public transport systems. These are not only a Hungarian aim but also target of the European transport policy. The third field of the utilization is the education. With the help of this model it is possible to show how a transport planning work is running. The new model give a more accuracy picture about a given public transport system than the common models; can show the efficiency of a studied network. It is also able to forecast the possible effects of a planned change or development like shown on the done experiment. Therefore the model is able to use in practice at real public transport systems. References [1] Abdelghany K.F., S. Mahmassani H.: Dynamic trip assignment-simulation model for intermodal transportation networks, Transportation Research Board 80 th Annual Meeting, Washington D. C p [2] Bakó A.: Determination of the Traffic Assignment, Applied Mathematical Journal, p (In Hungarian). [3] Cascetta E.: Transportation systems engineering for the design and evaluation of transit systems Proceedings of Advanced Course on Transit Networks, Rome p18. [4] Chriqui C.: Réseaux de transport en commun: Les problémes de cheminement et d accés, Center of Transport Research, University of Monteral, Publication p89. [5] Le Clerq: A public transport assignment method, Traffic Engineering and Control 1972/2 (14) p [6] Crisalli, U.: Dynamic transit assignment algorithms for urban congested networks, L. J. Sucharov: Urban Transport and the Environment for the 21 st century V. Computational Mechanics Publications p [7] De Cea, J., Fernandez, J. E.: Transit assignment for congested public transport systems: An equilibrium model, Transportation Science 1993/27. p [8] Henser, D. A., Button, K..J.: Handbook of Transport Modelling, Elsevier Science, Oxford, p412. [9] Dr. Nagy E., Dr. Szabó D.: Hungarian Transportation Handbook, Műszaki Könyvkiadó, Budapest, p

16 [10] Nuzzolo, A., Russo, F.: A Dynamic Network Loading model for transit services Proceedings of TRISTAN III. Conference, San Juan, Puerto Rico, p [11] Nuzzolo, A.: Schedule-based path choice models for public transport networks Proceedings of Advanced Course on Transit Networks, Rome p15. [12] Ortúzar, J. de D., Willumsen, L. G.: Modelling Transport, John Wiley & Sons, Chichester (England), p385. [13] Prileszky I., Fülöp G., Horváth B., Horváth G., Horváth R., Szabó L.: Public Transport Development Plan of Győr (in Hungarian). DHV Magyarország Kft, Budapest p186. [14] Prileszky I., Rixer A., Fülöp G., Horváth B., Horváth R.: Complex evaluation of the Public Trasport, Ministry of Transportation, Budapest p393. (in Hungarian). [15] Spiess, H., Florian, M.: Optimal strategies: A new assignment models for transit networks, Transportation Research B, 1989/2 (23) p