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Abstract
The optimal time-varying tolling is cumbersome for practical implementation due to the incomplete knowledge of toll determination and high costs for toll collection. Alternatively, a step toll is easier to implement than an optimal time-varying toll and could have lower operation costs and has been developed to reduce queuing time. In this paper, it is assumed that some drivers are willing to brake, while other drivers may pass the bottleneck near the end of the tolling period, and the braking drivers queue on the lanes and can impede other drivers. Two novel single-step-toll equilibrium models are developed with consideration of dropped capacity due to lanes occupied by the brakers. We found that some existing step-toll models are special cases of the proposed models. The toll level is further optimised to minimise either the maximal queue length or the total social cost. Finally, a numerical example is developed to illustrate the effect of the optimised toll on system performance.
Acknowledgements
The authors are grateful to thank Dr Zhiyuan Terry Liu for comments on an earlier version of this paper.
Funding
The work was supported by the Fundamental Research Funds for the Central Universities (2013JBM045), the National Natural Science Foundation of China (71371026, 71131001), the National Basic Research Program of China (2012CB725401), and the Fok Ying Tung Education Foundation (141081).