Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 910754, 15 pages
Research Article

Stochastic User Equilibrium Assignment in Schedule-Based Transit Networks with Capacity Constraints

1School of Architecture and Civil Engineering, Xiamen University, Xiamen 361005, China
2Research Center for Modern Logistics, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China
3Department of Systems and Industrial Engineering, The University of Arizona, Tucson, AZ 85721, USA

Received 9 June 2012; Revised 23 August 2012; Accepted 26 August 2012

Academic Editor: Wuhong Wang

Copyright © 2012 Wangtu Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a stochastic user equilibrium (SUE) assignment model for a schedule-based transit network with capacity constraint. We consider a situation in which passengers do not have the full knowledge about the condition of the network and select paths that minimize a generalized cost function encompassing five components: (1) ride time, which is composed of in-vehicle and waiting times, (2) overload delay, (3) fare, (4) transfer constraints, and (5) departure time difference. We split passenger demands among connections which are the space-time paths between OD pairs of the network. All transit vehicles have a fixed capacity and operate according to some preset timetables. When the capacity constraint of the transit line segment is reached, we show that the Lagrange multipliers of the mathematical programming problem are equivalent to the equilibrium passenger overload delay in the congested transit network. The proposed model can simultaneously predict how passengers choose their transit vehicles to minimize their travel costs and estimate the associated costs in a schedule-based congested transit network. A numerical example is used to illustrate the performance of the proposed model.