On seat capacity in traffic assignment to a transit network Fabien Leurent * Universite ´ Paris-Est, Laboratoire Ville Mobilite ´ Transport, Ecole des Ponts ParisTech, 6-8 avenue Blaise Pascal, Champs sur Marne 77455 Marne la Valle ´e Ce ´dex 2, France SUMMARY Seating or standing make distinct on-board states to a transit rider, yielding distinct discomfort costs, with potential influence on the passenger route choice onto the transit network. The paper provides a transit assignment model that captures the seating capacity and its occupancy along any transit route. The main assumptions pertain to: the seat capacity by service route, selfish user behaviour, a seat allocation process with priority rules among the riders, according to their prior state either on-board or at boarding. To each transit leg from access to egress station is associated a set of ‘service modes’, among which the riders are assigned in a probabilistic way, conditionally on their priority status and the ratio between the available capacity and the flow of them. Thus the leg cost is a random variable, with mean value to be included in the trip disutility. Computationally efficient algorithms are provided for, respectively, loading the leg flows and evaluating the leg costs along a transit line. At the network level, a hyperpath formulation is provided for supply-demand equilibrium, together with a property of existence and an method of successive averages equilibration algorithm. It is shown that multiple equilibria may arise. Copyright # 2010 John Wiley & Sons, Ltd. KEY WORDS: transit assignment; sitting behaviour; seated capacity; capacitated assignment; priority rules; line algorithms; route choice; network equilibrium 1. INTRODUCTION 1.1. Setting and literature review The planning of urban public passenger transport often requires considering the capacity constraints and congestion effects. In the past recent years, transit congestion has been given an increased attention from the research community in the science of transportation and traffic. Based on the Traffic Capacity and Quality of Service Manual (TCQSM [1]), we have identified seven types of congestion effects: (i) the vehicle traffic capacity of the infrastructure; (ii) the operating capacity on a transit route; (iii) vehicle capacity; (iv) the rider capacity of a transit service or route; (v) the passenger capacity of a station; (vi) the transit vehicle capacity of a station; (vii) the access and parking capacity for private vehicles at a station. One type of effect may take several forms: in particular, vehicle capacity can be broken down into seated capacity, rider capacity or boarding and alighting capacity at the doors. Figure 1 depicts the interplay of system components and capacity effects. Type (i): the vehicle traffic capacity of the infrastructure has been addressed by Spiess and Florian [2] who related the travel time (or cost) T a of link a to the flow volume x a by means of a travel time function, T a ¼ t a ðx a Þ. This formulation is appropriate for mild congestion, i.e. under capacity, either for the circulation of vehicles on the infrastructure by linking the journey time (cost) to the vehicle flow, or for the travel of riders by linking a discomfort cost to the number of riders on each vehicle. JOURNAL OF ADVANCED TRANSPORTATION J. Adv. Transp. 2012; 46:112–138 Published online 15 October 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/atr.146 *Correspondence to: Fabien Leurent, Universite ´ Paris-Est, Laboratoire Ville Mobilite ´ Transport, Ecole des Ponts ParisTech, 6-8 avenue Blaise Pascal, Champs sur Marne 77455 Marne la Valle ´e Ce ´dex 2, France. E-mail: fabien.leurent@enpc.fr Copyright # 2010 John Wiley & Sons, Ltd.