Common-Lines and Passenger Assignment in Congested Transit Networks Roberto Cominetti • José Correa Universidad de Chile, Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMR 2071 UCHILE-CNRS), Casilla 170/3 Correo 3, Santiago, Chile W e analyze a Wardrop equilibrium model for passenger assignment in general tran- sit networks, including the effects of congestion over the passengers’ choices. The model is based on the common-line paradigm, which is applied to general networks using a dynamic programming approach. Congestion is treated by means of a simplified bulk queue model described in the appendix. We provide a complete characterization of the set of equilibria in the common-line setting, including the conditions for existence and uniqueness. This characterization reveals the existence of ranges of flow in which a Braess-like paradox appears, and in which a flow increase does not affect the system performance as measured by transit times. The congested common-line model is used to state an equilibrium model for general transit networks, and to establish the existence of a network equilibrium. Introduction Passenger assignment models aim to describe the way users of a public transportation system employ the available infrastructure for traveling between differ- ent origins and destinations in the network. Several models have been proposed, differing with respect to the assumptions on passenger behavior, network structure, and modeling of congestion. Here is a short overview of work in this area. Earlier studies, such as those of Dial (1967), Fearnside and Draper (1971), and Le Clercq (1972), neglected congestion and assumed that passen- gers traveled along shortest paths on each origin- destination (OD) pair. The length of a path in this context corresponds to the total transit time including waiting as well as in-vehicle travel time. Later, con- sidering a single corridor served by a set of bus lines, Chriqui and Robillard (1975) introduced the notion of common-lines suggesting that passengers could bun- dle together a subset of the available lines in order to reduce the waiting and hence the overall tran- sit time. The assignment of passengers to bus lines was done proportionally to the nominal frequencies of each common-line. The extension of the common- line idea to general networks led Spiess (1984) and Spiess and Florian (1989) to introduce the notion of strategy, which was later expressed in graph-theoretic language by Nguyen and Pallottino (1988) under the denomination of hyperpath, namely, an acyclic sub- graph connecting a given OD pair. In these models— which can handle simultaneously several OD pairs, overlapping bus lines, and transfers at intermediate nodes on each trip—passengers are assumed to travel along shortest hyperpaths. Despite this generality, the models did not consider explicitly the increase in waiting times induced by congestion, and the assign- ment of passengers to bus lines was done propor- tionally to the nominal frequencies. However, Nguyen and Pallottino consider flow-dependent travel times, modeling the on-board crowding of buses which may affect the passengers’ choices. Transportation Science © 2001 INFORMS Vol. 35, No. 3, Summer 2001 pp. 250–267 0041-1655/01/3503/0250$05.00 1526-5447 electronic ISSN