Journal of Applied Mathematics
Volume 2013 (2013), Article ID 696481, 11 pages
Research Article

Stochastic Congestion Pricing among Multiple Regions: Competition and Cooperation

1Centre for Maritime Studies, National University of Singapore, Singapore 118411
2School of Business, Central South University, Changsha, Hunan 410000, China
3Department of Mathematics, School of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Received 17 January 2013; Accepted 3 March 2013

Academic Editor: Xiaoning Zhang

Copyright © 2013 Hua Wang 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.


Previous studies of road congestion pricing problem assume that transportation networks are managed by a central administrative authority with an objective of improving the performance of the whole network. In practice, a transportation network may be comprised of multiple independent local regions with relative independent objectives. In this paper, we investigate the cooperative and competitive behaviors among multiple regions in congestion pricing considering stochastic conditions; especially demand uncertainty is taken into account in transportation modelling. The corresponding congestion pricing models are formulated as a bilevel programming problem. In the upper level, congestion pricing model either aims to maximize the regional social welfare in competitive schemes or attempts to maximize the total social welfare of multiple regions in cooperative schemes. In the lower level, travellers are assumed to follow a reliability-based stochastic user equilibrium principle considering risks of late arrival under uncertain conditions. Numerical examples are carried out to compare the effects of different pricing schemes and to analyze the impact of travel time reliability. It is found that cooperative pricing strategy performs better than competitive strategy in improving network performance, and the pricing effects of both schemes are quite sensitive to travel time reliability.