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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 679719, 8 pages
Research Article

Parking Pricing and Model Split under Uncertainty

1State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China
2MOE Key Laboratory for Urban Transportation Complex Systems Theory, Beijing Jiaotong University, Beijing 100044, China

Received 20 June 2013; Revised 7 January 2014; Accepted 8 January 2014; Published 19 February 2014

Academic Editor: Elmetwally Elabbasy

Copyright © 2014 Chengjuan Zhu 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.


In order to investigate different route choice criteria in a competitive highway/park-and-ride (P&R) network with uncertain travel times on the road, a bilevel programming model for solving the problem of determining parking fees and modal split is presented. In the face of travel time uncertainty, travelers plan their trips with a prespecified on-time arrival probability. The impact of three route choice criteria: the mean travel time, the travel time budget, and mean-excess travel time, is compared for parking pricing and modal split. The model at user equilibrium is described as a minimization model. And the analytic solutions are given. Analytic solutions show that both flow and travel time at equilibrium are independent of the price difference of travel expense on money. The main findings from the numerical results are elaborated. While given a confidence level, the flow on the highway changed significantly with the criteria, although the differences of the travel times are small. Travelers can be guided to choose their modes coordinately by improving the quality of the transit service. The optimal parking fees can be affected markedly by the confidence level. Finally, the influence of the log-normal distribution parameters is tested and analyzed.