Abstract. 1 Introduction

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1 Intermodal transportation in urban framework: a discrete-events simulative approach A. Di Febbraro", V. Recagno* & S. Sacone" ^Department of Communications, Computer, and System Sciences Dipartimento di Ingegneria Elettrica, University of Genova, Via airopera Pia 11 a, Genova, Italy Abstract In the last years, a promising research subject has been the integration of the transportation services present in an area taken into account, in order to realise intermodality in transportation. In this paper, an urban integrated transportation network is considered. The behaviour of the network is described by means of a discrete-event model which is intended to be the basis of an on-purpose designed traffic simulator. Finally, some control strategies are proposed to guarantee the regularity of the transportation services, i.e., the fulfilment of the timetable. 1 Introduction Intermodal transportation can be defined as the serial use of different means of transportation to move passengers and/or freight from a place to another. Up to now greater interest has been devoted to intermodal freight transportation, e.g. Kondratowicz [1], Guelat, Florian & Crainic [2], even though intermodal passenger transportation well applies to urban and suburban frameworks. Urban public transportation services usually consist in buses, underground, and railway and the integration among them and between public and private urban transportation can be carried out by designing a transportation network, in which there are stations where it is possible to switch from a means of transport to another one. The subject of this paper is about modelling a network of this kind and simulating its behaviour in order to analyse its performances and to design control strategies.

2 202 Railway Design and Management For the novel transportation system under study, a peculiar discrete event model has been developed to describe and optimise its behaviour. Moreover, it is supposed that passengers can approach the urban integrated transportation system using any means of transport. This is due to the particular structure of the model designed for the network, which provides for a node which constitutes the 'interface' between the urban transportation network and the outer world. To model also the arrivals of passengers by private means of transport, the parking areas located near the nodes of the network have been taken into account. In these areas the passengers can leave their private means, and then enter the public transportation network. Due to the peculiar aspects of the system to study, simulation seems to be the most suitable way of modelling its discrete event characteristics. Statistical distributions are given for the occurrences of the different kinds of events, e.g. Banks & Carson [3]. The simulation of the functioning of the integrated transportation system yields a statistical analysis of such variables of interest as the real travel times on the links, the mean vehicle delays, and the vehicle break-downs. Moreover, considering the whole intermodal transportation system to be a discrete event process, it is easy to determine the variables which affect significantly the behaviour of the system and, consequently, the optimisation objectives given. Therefore, once defined the discrete event model of the system, it is possible to analyse any performance index related to the available output statistics. The behaviour of the discrete event system modelling the transportation network is studied by means of an on-purpose designed simulation tool. Some control strategies, based on the measure of the delays of the transport means, are proposed with the objective of guaranteeing the regularity of the transportation services, i.e., the fulfilment of the timetables for the three modes of transport given as inputs to the simulator. 2 The model for the intermodal transportation system As it is well known in the literature, during the planning activity a transportation system can be divided into two different subsystems: the design system and the activity system. The first one deals with the peculiar aspects of the transportation system case study; the second one represents the outer world, and it is taken into account only in terms of the relationships between itself and the design system. The design system is divided into three more parts: the demand system, which represents the needs and the behaviour of the users, the supply system, which includes all what concerns the service production from the infrastructure to the planning rules of the whole system, and the demand-supply interaction system, which represents the effects that the demand can induce on the supply, i. e., how a congestion due to a demand increase causes an augmentation of the transportation system cost.

3 Railway Design and Management 203 In this work the demand model is neglected, so we refer the reader to some bibliography about this topic (for example Kanafani [4], Ben Akiva & Lerman [5], Cascetta & Cantarella [6]). As briefly seen in the introduction, the case under study is the transportation network of an Italian city which includes three different kinds of transport means: underground, railway, and bus. Moreover, it is supposed that passengers can approach the urban integrated transportation system using any means of transport, private cars included. Under these assumptions the network is represented as an oriented graph composed of three fundamental entities, which are macronodes, nodes, and links. A macronode is an intermodal station, that is, a place where people can change mode of transport, or simply enter the transportation system. In other words, a macronode is a point where underground, railway, and bus lines intersect. A node is a station for a single transportation mode, so a node can only exist as a part of a particular macronode. Therefore, a macronode is composed of one or more nodes connected by inner links (footpaths). A link is a unidirectional transportation line connecting two macronodes and devoted to a single transportation mode. Since in the network considered there are three possible transportation means, links are divided into the three following classes: a) B-links : which represent bus lines; b) R-links : which represent railway lines; c) U-links : which represent underground lines. The network under study is composed of N macronodes and L links; macronodes 1,...,N-1 represent the real stations of the transportation system considered, while the last macronode, i.e., macronode N, is a 'virtual' macronode, as it is not a real station, but it represents the outer world with respect to the network. In other words, each macronode which connects the urban area with its surroundings has a link towards macronode N. This feature allows not only to model each urban network as a closed network, but also to extend the representation adopted to areas wider than the urban ones. Another advantage of using a closed network stands in the fact that it is possible to apply particular storage methods for closed graphs reducing sensibly the computational load. Then, macronode n, n=l,.., N, has In input links and On output links; for each macronode the types of its input and output links (U, R, or B) are specified. Clearly, each macronode n, n=l,..,n, can have at most six links in common with another macronode m, m=l,..,n, m#n. The mean travel times of the inner links of each macronode are known and constant. The travel times of the links between two macronodes are a- priori known and updated in real-time on the basis of traffic conditions. In the same way, the travel times by car of those links where private traffic is allowed are kept up-to date. Knowing all these times allows to estimate at each time

4 204 Railway Design and Management instant the shortest path between each pair of macronodes of the network, and this information is made available to the user. The fundamental entities of the model consist of those defined before as network entities (macronodes, nodes, and links) plus the transportation means; these entities are also the main components of the simulation program. Moreover, the model includes static quantities (parameters) and dynamic quantities (state variables) associated with each class of entities (see, for further details, Di Febbraro, Recagno & Sacone [7]). 3 Discrete-event representation To face properly the problem of representing such a network, a thorough study of the possible modelling techniques has been carried out. As a result, it seems suitable to model the whole network as a Discrete Event Dynamic System. Discrete event systems respond to the following characteristics: they are discrete in time and space, asynchronous, and modular. Moreover, discrete event systems may include control strategies and communication systems, to enable some particular controllable events or to signal the occurrence of observable events between a pair of modules. Ruling communication and control strategies, it is possible to make the event flow fit the project requirements. In this context, the described intermodal urban transportation network is represented as a discrete event system. Recently, discrete event representation has been used to model various transportation systems; examples of such applications can be found in Di Febbraro & Ferrara [8], Casalino et al.[9]. Starting from the model described in the previous section, events which rule the transportation system flow have been selected as follows. The events that describe the behaviour of the system and then determine the evolution of the simulation tool, which will be described in the next section, are divided into two main classes, which are: i) events that describe the nominal traffic conditions, such as the leaving/arrival of a transportation means from/to a node; ii) events that represent unpredictable conditions affecting the system, such as the break-down of a vehicle, critical traffic conditions on B-links, etc. Each kind of event is associated with an operational procedure which, once invoked, modifies the discrete event model state variables in dependence of the event occurred. Such procedure has to insert in the active event list (i.e. the increasing time sorted list of those events whose occurrence times are known) all the events which will occur as a consequence of the current event. Before starting a simulation session, it is necessary to build an active event list including those events for which the occurrence times are known when the session starts. During the simulation, the active event list is continuously

5 Railway Design and Management 205 examined and updated, by processing and eliminating, time after time, the event which occupies the head of the list. 4 Description of the simulation tool The simulation tool realised consists of three fundamental blocks: i) an input interface; ii) a passenger information system; iii) a block which uses the discrete event simulation kernel to create the statistics of the system behaviour and to design suitable control strategies. Network topology Input statistics Time tables for the 3 User's^ request \ \ r \ f Input interface 1 G / / Passenger information system i Shortest path algorithm \ \\ ^ ^ Data base ^»-~^ \ / 1 Y Shortest path Figure 1: Scheme of the simulation tool.

6 206 Railway Design and Management In Figure 1 the complete scheme of the simulation tool, putting into evidence the division among the three fundamental blocks, is shown. The input to the program is composed by the following variables: network topology and timetables for the three transportation modes; statistics of: links travel times, stopping times in the nodes, time interval between the arrival at the end of a link and the beginning of the stopping time in a node, time interval between the end of a stop in a node and the departure from a node, duration of the different kinds of perturbations, time interval between two perturbations. The input data are processed by a suitable interface and transferred to a data base which contains the whole static information about the transportation network. The other two blocks of the simulation program get the parameters of the system from this data base. The second block of the simulation tool is the information system; this system receives as an input the request of the user who needs to move from a macronode to another macronode of the network. The information system retrieves the static quantities of the transportation system in the data base and the real-time dynamic quantities in the DEDS. This set of data is the input of a shortest-path algorithm which determines the shortest multimodal path to be followed to move from the origin to the destination requested by the user. The first component of the third block is the DEDS, that is, the discrete event system which models the dynamic behaviour of the transportation network under study. The evolution of this system is reproduced by means of discrete event simulation techniques, as mentioned in the previous section. The output data of a simulation run are: a simulation trace; the following output statistics: links travel time means and variances, stopping time means and variances for each transportation mode and for each station, delay time means and variances for each transportation mode, for each station, and for each path, means and variances of the number of severe perturbations for each transportation mode and for each path. The output statistics above can be used to analyse and optimise the performances of the transportation system. The variety of sensible performance indexes is wide, so the choice of them should be made according to the particular purposes of the simulation analysis. In this case, the main objective is that of validating the timetables for the intermodal transportation network given as inputs, finding the best integrated timetable. This should be done in the fulfilment of the different timetables, as explained in the next section. 5 Control strategies In such a transportation system as the one described in this paper, when one neglects all the modelling aspects relevant to the single passengers moving in

7 Railway Design and Management 207 the network, just as we have done, it seems sensible to aim at guaranteeing the regularity of transport services. This can be achieved by designing suitable control strategies. The proposed criterion to analyse the performances of the intermodal transportation system is based on the measures of the delays of the transport means associated with the different transport modes with respect to the given timetables. On this basis, two different kinds of control strategies can be applied in presence of delay of some transport means. The first, trivial one is that of making the transport means which are late traverse the links in the minimum travel time until they achieve again the fulfilment of the timetable. This 'acceleration* is possible as the travel times on the links given by the timetables are always quite over dimensioned, so as to regain some short delay. The second control strategy proposed in the event of a late transport means consists in comparing its delay with a suitable threshold determined taking into account the system conditions, the possibility of making another transport means enter the network, and the economic aspects. If such a threshold is overcome by the delay, then a transport means of the same mode of the late one is made to enter the system, at a node downstream with respect to the late means along the path it is following. Such a node is chosen by running an optimisation procedure which takes into account the positions of the nearest depots and terminal stations, and the availability of inactive transport means of the mode needed. 6 Simulation results In order to analyze the behavior of the transportation system described, simulation experiments have been performed, and in this section, an applicative example is reported. 12 time (h) Figure 2: Mean bus delays with and without control

8 208 Railway Design and Management The considered transportation network is composed of 21 macronodes and 80 links. As regards the transportation lines, the network comprehends 24 bus lines, 8 railway lines, and 4 underground lines; the timetable presents a number of runs up to 20/hour during the peak hour for each transportation mode. In figure 2, a comparison is made between the behavior of the system without control application (plain line) and its behavior when applying the first control strategy (dashed line). 7 Conclusions In this paper, the problem of modelling an intermodal transportation system has been dealt with. The considered transportation system has been modelled as a discrete event system, whose behaviour has been studied by means of an on-purpose designed discrete event simulator. Such a simulation tool consists of three fundamental modules: i) input interface; ii) passenger information system; iii) discrete event simulation kernel. Only parts i) and iii) have been described in detail in this paper. Work is in progress to generalise the model to include the representation of a communication system (possibly wireless) underlying the transportation network itself. References 1. Kondratowicz, L.J. Simulation Methodology for Intermodal Freight Transportation Terminals, Simulation, 1990, 55, Guelat, J., Florian, M., & Crainic, T.G. Multimode Multiproduct Network Assignment Model for Strategic Planning of Freight Flows, Transportation Science, 1990,24, Banks, J. & Carson, J.S. Discrete-Event System Simulation, Prentice-Hall, Englewoods Cliffs, Kanafani, A. Transportation Demand Analysis, McGraw-Hill, New York, Ben Akiva, M. & Lerman, H. Discrete Choice Analysis, MIT Press, Cambridge, MA, Cascetta, E. & Cantarella, G.E. Modelling dynamics in transportation networks: State of the art and future developments, Simulation Practice and Theory, November 1993, Di Febbraro, A., Recagno, V. & Sacone, S. Discrete event simulation of an intermodal transportation system, Proc. European Simulation Multiconference, Barcelona, Spain, 1994, in press. 8. Di Febbraro, A. & Ferrara, A. Performance analysis of underground railway networks through continuous-time and discrete-event simulation, Proc. 3rd European Simulation Congress, Edinburgh, UK, September Casalino, G., Di Febbraro, A., Ferrara, A., Minciardi, R. & D. Nicoletti, Underground modelling and control: discrete-event approach, Concise Encyclopedia of Traffic and Transportation Systems, Pergamon Press, Oxford, 1991, pp