Congestion behavior and tolling strategies in a bottleneck model with exponential scheduling preference

Chuanyao Li; Yichao Lu; Yuqiang Wang; Gege Jiang; Chuanyao Li; Yichao Lu; Yuqiang Wang; Gege Jiang

doi:10.3934/era.2023053

Electronic Research Archive

2023, Volume 31, Issue 2: 1065-1088. doi: 10.3934/era.2023053

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Congestion behavior and tolling strategies in a bottleneck model with exponential scheduling preference

1.
School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China
2.
School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518000, China

Received: 03 October 2022 Revised: 24 November 2022 Accepted: 29 November 2022 Published: 13 December 2022

The bottleneck model has been widely used in the past fifty years to analyze the morning commute. To reduce the complexity of analysis, most previous studies adopted discontinuous scheduling preference (DSP). However, this handling destroys the continuity in departure rate and differentiability in travel time and cumulative departures. This paper considers an exponential scheduling preference (ESP), which supposes the unit schedule delay cost for commuters exponentially changes with time. With this scheduling preference, we analytically derive solutions and economic properties of user equilibrium and social optimum in the bottleneck model. The first-best, time-varying toll and the optimal single-step toll scheme with ESP are also studied. Results indicate that ESP eliminates the discontinuity in departure rate and non-differentiability in travel time and cumulative departures, which makes the process of morning commute smooth. The ignorance of ESP will lead to underestimation in the queueing time and bias in travel behavior analysis and policymaking.
- the bottleneck model,
- traffic congestion,
- exponential scheduling preference,
- user equilibrium,
- social optimum
Citation: Chuanyao Li, Yichao Lu, Yuqiang Wang, Gege Jiang. Congestion behavior and tolling strategies in a bottleneck model with exponential scheduling preference[J]. Electronic Research Archive, 2023, 31(2): 1065-1088. doi: 10.3934/era.2023053

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Abstract

The bottleneck model has been widely used in the past fifty years to analyze the morning commute. To reduce the complexity of analysis, most previous studies adopted discontinuous scheduling preference (DSP). However, this handling destroys the continuity in departure rate and differentiability in travel time and cumulative departures. This paper considers an exponential scheduling preference (ESP), which supposes the unit schedule delay cost for commuters exponentially changes with time. With this scheduling preference, we analytically derive solutions and economic properties of user equilibrium and social optimum in the bottleneck model. The first-best, time-varying toll and the optimal single-step toll scheme with ESP are also studied. Results indicate that ESP eliminates the discontinuity in departure rate and non-differentiability in travel time and cumulative departures, which makes the process of morning commute smooth. The ignorance of ESP will lead to underestimation in the queueing time and bias in travel behavior analysis and policymaking.

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