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，但实施社会福利或收益最优的动态收费往往不切实际。大多数现实世界的拥堵定价部署（包括纽约市近期推出的项目）都依赖于显著更简单、通常是静态的收费方式。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，会产生多大的收益和社会福利损失？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回答这一问题：一是包含公共交通替代选择的Vickrey瓶颈模型，二是基于宏观基本图（MFD）的城市尺度扩展模型。在这两种模型中，我们首先刻画了收益最优的静态与动态收费策略——这一议题在先前研究中关注有限。在最坏情况下，收益最优静态收费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，且系统成本至多是最小可实现系统成本的两倍；其中瓶颈模型中的理论保证比MFD模型更强且更具普适性。我们进一步利用旧金山湾区和纽约市的真实数据集进行数值验证，结果表明确实最优静态收费能达到动态最优收益的约80-90%，同时产生的系统总成本仅比最小可实现系统成本高出8-20%。