Departure Time Choice Equilibrium and Tolling Strategies for a Bottleneck with Stochastic Capacity

Jiancheng Long (), Hai Yang () and W. Y. Szeto ()
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Jiancheng Long: School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei 230009, China
Hai Yang: Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong
W. Y. Szeto: Department of Civil Engineering, The University of Hong Kong, Hong Kong

Transportation Science, 2022, vol. 56, issue 1, 79-102

Abstract: This paper develops a bottleneck model in which the capacity of the bottleneck is assumed to be stochastic and follow a general distribution that has a positive upper bound. The user equilibrium principle in terms of mean trip cost is adopted to formulate commuters’ departure time choice in the stochastic bottleneck. We find that there exist five possible equilibrium departure patterns, which depend on both commuters’ unit costs of travel time, schedule delay early and late, and the uncertainty of the stochastic capacity of the bottleneck. All possible equilibrium departure patterns are analytically derived. Both the analytical and numerical results show that increasing the uncertainty of the capacity of the bottleneck leads to an increase of commuters’ individual mean trip cost. In addition, both a time-varying toll scheme and a single-step coarse toll scheme are designed within the proposed stochastic bottleneck model. We provide an analytical method to determine the detailed toll-charging schemes for both toll strategies. The numerical results show that the proposed toll schemes can indeed improve the efficiency of the stochastic bottleneck in terms of decreasing mean total social cost, and the time-varying toll scheme is more efficient than the single-step coarse toll scheme. However, as the uncertainty of the capacity of the bottleneck increases, the efficiency of the time-varying toll scheme decreases, whereas the efficiency of the single-step coarse toll scheme fluctuates slightly.

Keywords: bottleneck model; no-toll equilibrium; time-varying toll; single-step coarse toll; stochastic capacity (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:56:y:2022:i:1:p:79-102

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