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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 136872, 8 pages
Research Article

Multimodal Network Equilibrium with Stochastic Travel Times

1MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China
2Centre for Infrastructure Systems, School of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639798

Received 21 April 2014; Accepted 17 June 2014; Published 3 July 2014

Academic Editor: Ricardo Femat

Copyright © 2014 M. Meng 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.


The private car, unlike public traffic modes (e.g., subway, trolley) running along dedicated track-ways, is invariably subject to various uncertainties resulting in travel time variation. A multimodal network equilibrium model is formulated that explicitly considers stochastic link capacity variability in the road network. The travel time of combined-mode trips is accumulated based on the concept of the mean excess travel time (METT) which is a summation of estimated buffer time and tardy time. The problem is characterized by an equivalent VI (variational inequality) formulation where the mode choice is expressed in a hierarchical logit structure. Specifically, the supernetwork theory and expansion technique are used herein to represent the multimodal transportation network, which completely represents the combined-mode trips as constituting multiple modes within a trip. The method of successive weighted average is adopted for problem solutions. The model and solution method are further applied to study the trip distribution and METT variations caused by the different levels of the road conditions. Results of numerical examples show that travelers prefer to choose the combined travel mode as road capacity decreases. Travelers with different attitudes towards risk are shown to exhibit significant differences when making travel choice decisions.