## Network Design Model for Generating Transit Timetable

### Authors

P Coppola, University of Rome Tor Vergata, IT

### Description

A model for obtaing the User-optimal timetables of ex-urban transit services is presented. With respect to the models presented in the literature,here the impact that timetable has on users path choices is explicitly simulated.

### Abstract

It is well-known that timetables setting for a transit networks can affect, to a great extent, the quality, the effectiveness and the efficiency of the Public Transportation (PT) system, both on the users and on the operator perspectives. According to Ceder and Wilson (1986) the general transit network-design problem can be split into five sequential phases: 1) identification of the routes of the transit lines; 2) line-frequencies optimization; 3) timetable setting; 4) vehicle scheduling; 5) crew scheduling. Thus, given the routes and frequencies of the transit lines the problem of generating a timetable consists of identifying the ?optimal? departure time of a number of operating on different lines in a given reference period, subject to constraints on vehicles and crew availability.

It is worth to distinguish between the two cases of high-frequency and the low-frequency transit network. In the first case (typically the urban case), given the high frequency of the transit lines and the random arrival of travellers at stops, the marginal benefit in terms of waiting and transfer time that might derive from adjusting timetable, is minimal. In facts, in high-frequency systems, it is common practice to optimise, first, the vehicles scheduling in order to reduce the operating costs (for example a reduction of the size of the fleet) and, then, derive accordingly the timetable. On the other hand, in the case of medium/low-frequency system (typically the case of ex-urban PT networks), the optimisation of timetable can highly reduce travellers waiting time and transfer time as well as can avoid overcrowded vehicles. In this paper we focus on low-frequency transit system.

In order to generate timetable in such systems, different model specifications have been proposed in the literature. These can be grouped in two main classes: one including models aiming at maximizing the number of simultaneous bus arrivals at the connection (transfer) nodes of the network (see for instance, Desilet and Rousseau, 1992; Voss, 1992; Ceder and Tal, 2001), another including models aiming at matching vehicles departure time with travellers desired departure and/or arrival time at stops (see for instance Ceder, 1986, 2001; Russo, 1998). In both classes of models, path flows on the transit network are assumed to be invariant with respect to timetable. In other words, it is not considered that a variation of the timetable can modify travelers path choices.

The model formulation here presented, takes into consideration such feedback. In order to simulate how travelers choices vary with the timetable the schedule-based approach to dynamic transit network modeling is followed (Nuzzolo et al., 2001; Nuzzolo and Wilson, 2003). This allows, on the supply side, an explicit time-space representation of the transit network, and, on the demand side, the simulation of travelers path choice depending on their desired departure time from origin.

The model is based on a non-linear programming formulation in which the objective function to minimize is given by the total generalized cost perceived by travelers, that is the product of the path flows times the path generalized cost computed as the weighted sum of on-board time, transfer time, early and late scheduled delay (Abkowitz, 1981).

A bi-level algorithm is developed to solve the problem: at the first level timetable is generated by minimizing the objective function for a given pattern of path flow using an heuristic technique based on local search; at the second level, given the optimal timetable previously generated, the new path flows are estimated by means of a dynamic schedule based transit assignment model. This model is iterated until convergence is achieved.

The efficiency of this algorithm is demonstrated through applications to different small-scale example networks. Preliminary results have shown significant reductions of the total generalized travel cost using the proposed model formulation. Finally, in the paper, an application to the realistic case study of the railways transit network of the metropolitan area of Naples (Italy) is illustrated.

Essential References

Abkowitz MD (1981) An analysis of the commuter departure time decision. Transportation: 283-297

Ceder A, Wilson NHM (1986) Bus Network Design. Transportation Research 20B: 331-344.

Ceder A (1986) Methods for Creating Bus Timetables. Transportation Research 21A: 59-83.

Ceder, A., Tal, O. (2001) Designing synchronization into bus timetables. Journal of Transportation Research Board 1760.

Desilet A, Rousseau J (1992) Syncro: A Computer-Assisted Tool for the Synchronization of Transfer in Public Transit Networks. In: Desrochers, Rousseau (eds) Computer-Aided Transit Scheduling. Springer-Verlag, Berlin.

Russo F (1998) A model for schedule optimization in an intercity transportation system. In: Mellitt et al. (eds) Computer in Railways VI. WIT Press, Boston-Southampton.

Voss S (1992) Network Design Formulation in Schedule Synchronization. In: Desrochers, Rousseau (Eds.) Computer-Aided Transit Scheduling. Springer-Verlag, Berlin, pp 137-152.

Nuzzolo A, Russo F, Crisalli U (2001) Dynamic schedule-base assignment models for public transport networks. Franco Angeli Ed., Italy

Wilson NHM, Nuzzolo A (2003) The schedule-based approach in dynamic transit modeling: theory and applications. Kluwer Academic Publisher, Dordhrecht-Boston-London.

#### Publisher

Association for European Transport