Simple vs. Optimal Congestion Pricing

2026-02-24

AI Summary

This study investigates the welfare and revenue gaps between widely implemented static congestion pricing and theoretically optimal dynamic pricing in urban road networks. Building upon the Vickrey bottleneck model extended with a macroscopic fundamental diagram (MFD) framework and calibrated with real-world data from the San Francisco Bay Area and New York City, the paper provides the first systematic characterization of both static and dynamic tolling strategies under revenue-maximizing objectives. Theoretically, it establishes that static pricing guarantees at least 50% of the revenue achievable by dynamic pricing in the worst case. Empirically, static pricing attains 80–90% of the optimal dynamic revenue, while incurring only 8–20% higher total system costs. These findings offer both theoretical performance guarantees and empirical validation for the practical efficacy of static congestion pricing.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

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.

Problem

• congestion pricing
• static tolling
• dynamic tolling
• revenue loss
• welfare loss

Innovation

• congestion pricing
• static tolling
• dynamic tolling
• Vickrey bottleneck model
• Macroscopic Fundamental Diagram