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.

翻译：拥堵定价已成为缓解交通拥堵的有效工具，然而实施社会福利或收益最优的动态收费方案往往不切实际。大多数现实世界的拥堵定价部署（包括纽约市近期推行的项目）都依赖于更为简单且通常为静态的收费方式。这种差异引出了一个关键问题：当现实交通系统采用静态定价而非最优动态定价时，会产生多大的收益与社会福利损失？我们通过分析两种经典框架中静态（简单）与动态（最优）拥堵定价方案的性能差距来探讨这一问题：即包含公共交通替代选择的Vickrey瓶颈模型及其基于宏观基本图（MFD）的城市尺度扩展模型。在这两个模型中，我们首先刻画了收益最优的静态与动态收费策略——这一方向在先前研究中关注有限。在最坏情况下，收益最优的静态收费方案能在广泛的实际相关参数范围内实现至少一半的动态最优收益，且系统成本至多达到最低可实现系统成本的两倍；其中瓶颈模型的理论保证比MFD模型更强且更具普适性。我们进一步基于旧金山湾区与纽约市的真实数据集，通过数值结果验证了理论保证：数据显示静态收费方案可实现约80-90%的动态最优收益，同时产生的总系统成本仅比最低可实现系统成本高出8-20%。