[论文解读] Simple vs. Optimal Congestion Pricing

Devansh Jalota, Sharon Di+1 more|arXiv (Cornell University)|Feb 25, 2026

Transportation Planning and Optimization被引用 0

一句话总结

本文比较了在有外部选项和基于 MFD 的城市系统中的Vickrey瓶颈模型下，静态以收入最大化为目标的收费与动态（最优）收费，并导出闭式解的静态策略，界定其相对于动态收费的收入与福利差距的上界。

ABSTRACT

Congestion pricing has emerged as an effective tool for mitigating traffic congestion, yet implementing welfare or revenue-optimal dynamic tolls is often impractical. Most real-world congestion pricing deployments, including New York City's recent program, rely on significantly simpler, often static, tolls. This discrepancy motivates the question of how much revenue and welfare loss there is when real-world traffic systems use static rather than optimal dynamic pricing. We address this question by analyzing the performance gap between static (simple) and dynamic (optimal) congestion pricing schemes in two canonical frameworks: Vickrey's bottleneck model with a public transit outside option and its city-scale extension based on the Macroscopic Fundamental Diagram (MFD). In both models, we first characterize the revenue-optimal static and dynamic tolling policies, which have received limited attention in prior work. In the worst-case, revenue-optimal static tolls achieve at least half of the dynamic optimal revenue and at most twice the minimum achievable system cost across a wide range of practically relevant parameter regimes, with stronger and more general guarantees in the bottleneck model than in the MFD model. We further corroborate our theoretical guarantees with numerical results based on real-world datasets from the San Francisco Bay Area and New York City, which demonstrate that static tolls achieve roughly 80-90% of the dynamic optimal revenue while incurring at most a 8-20% higher total system cost than the minimum achievable system cost.

研究动机与目标

• 在现实世界拥堵定价中，福利/收入最优的动态收费与可部署的静态收费之间的实际差距提供动机。
• 在Vickrey瓶颈模型（含外部选项）和基于MFD的城市系统中，表征静态和动态收费策略的收入最优性。
• 在静态收费下对收入和总系统成本提供相对于动态基准的理论保证。
• 通过对旧金山湾区与纽约市案例的数值实验来支持发现。

提出的方法

• 用Vickrey瓶颈模型与外部选项（公共交通）建立模型并推导均衡收费结果。
• 推导闭式的收入最优静态收费与收入最优动态收费；展示动态收费具有梯形结构。
• 将分析扩展到基于MFD的城市尺度框架并表征收入最优的动态收费。
• 建立最坏情况界：在瓶颈情形下静态收入最优收费至少达到动态收入的1/2；在系统成本的最小值下至多为2倍；在MFD情形下有类似但较弱的界限。
• 用实际数据集进行数值验证（旧金山湾区桥梁、纽约市拥堵区）。

Figure 1 : Equilibrium waiting time profiles in the bottleneck model without an outside option (left) and with a public transit outside option in a mixed-mode equilibrium where both car and transit are used (right) in the setting when $\mu<\lambda$ . The slopes $e$ and $L$ denote the normalized sche

实验结果

研究问题

• RQ1 在带有外部选项的瓶颈模型中，静态收入最优收费与动态（最优）收费之间的收入差距是多少？
• RQ2 在有外部选项的瓶颈模型中，静态与动态收费对福利/系统成本的影响各自为何？
• RQ3 在基于MFD的城市系统中，静态与动态收费在收入与总系统成本方面的对比如何？
• RQ4 在实际参数范围内，静态收费是否接近动态收费；在哪些条件下差距扩大？
• RQ5 将结果与实际部署如SF湾区与纽约市的情况对齐？

主要发现

• 在瓶颈模型中，静态收入最优收费在各种参数情形下至少达到动态收入的二分之一，在许多实际情形下至少达到三分之二。
• 当公共交通选项未显著低于驾车吸引力时，静态收入最优收费的系统成本最多是最优解的两倍。
• 在MFD框架下，静态收入最优收费在大多数情形下至少达到动态收入的三分之二，且系统成本至少等于最小值的两倍的上界在多数情形成立（相较于瓶颈情形保证较弱）。
• 数值结果显示静态收费在动态最优收入方面大致达到80-90%，在对于实际相关情形下总系统成本最高增加8-20%。
• 在对真实部署进行评估时，当前静态收费对应的参数情形是静态收入最优收费接近约98%的动态收入，且成本比最小值高约3%。
• 一个关键决定因素是系统最大吞吐量与期望用户到达率之比；比值接近1时能获得更高的收入比例，但成本差距也更大；而类似纽约市的情形若比值较小，差距较小。
• 总体而言，简单的静态收费在收入与系统成本等指标上表现稳健，在实际应用中对动态收费可以接近最优。

Figure 2 : Depiction of the revenue optimal dynamic tolling policy. Here, $[t_{A}^{*},t_{D}^{*}]$ denotes the equilibrium interval over which users pass the bottleneck under the dynamic revenue-optimal tolling policy $\tau_{d}^{*}(\cdot)$ , analogous to the no-toll equilibrium interval $[t_{A},t_{D}