Departure time choice equilibrium and tolling strategies for a bottleneck with continuous scheduling preference

This paper develops a bottleneck model with continuous scheduling preference (CSP), which assumes that the unit cost of schedule delay penalty functions have continuously linear forms. In particular, the unit cost of schedule delay early is non-increasing with respect to arrival time, while the unit cost of schedule delay late is non-decreasing with respect to arrival time. We analyze the departure time choice equilibrium of commuters and find that the proposed bottleneck model with CSP is capable of eliminating the discontinuity of the departure rate curve, which occurs in the bottleneck model with discontinuous scheduling preference (DSP). In addition, the first-best and second-best congestion tolling strategies are designed in the bottleneck model with CSP. The analytical closed-form solutions of the bottleneck model with CSP under the time-varying toll, single-step coarse toll and multi-step toll are obtained and their effects on system performance are investigated. Finally, numerical examples are developed to illustrate the properties of the proposed models. Results shed light into the necessity of considering CSP in travel behavior analysis and congestion management. The ignorance of CSP can lead to overestimate of commuters’ bottleneck queuing time and the total system travel cost (TSTC), which finally reduces the efficiency of congestion tolling strategies.