拓扑感知的拥堵定价：基于Forman-Ricci曲率的鲁棒需求路由

中文摘要 AI 辅助

拥堵定价被广泛用于提高交通网络效率，因为个体分散的路径选择可能导致系统级低效。庇古税（Pigouvian tolls）能达到系统最优，但依赖于需求，且在需求变化时可能失效，尤其是在结构上关键的瓶颈边上。我们提出了一种对控制（Wardrop）均衡的Beckmann势进行拓扑感知正则化的方法，通过将预先计算的庇古税与基于Forman-Ricci曲率（FRC）的离线结构惩罚相结合，该曲率能捕捉瓶颈结构。我们证明了由此产生的均衡是良定义的，更强的正则化会减少受惩罚边上的流量，且效率损失取决于结构惩罚与最优庇古税的接近程度。在八个真实世界网络上，针对定向和均匀需求扰动的实验表明，瓶颈流量减少且效率接近最优。FRC在显著降低计算成本的情况下实现了与边介数（edge betweenness）相当的流量减少，使其成为经典拥堵定价的实用、稳健的补充。

英文摘要

Congestion pricing is widely used to improve transportation network efficiency where individual decentralized route choices can lead to system-level inefficiencies. Pigouvian tolls achieve the system optimum but depend on demand and can lose effectiveness under demand shifts, particularly on structurally critical bottleneck edges. We propose a topology-aware regularization of the Beckmann potential governing the (Wardrop) equilibrium by augmenting precomputed Pigouvian tolls with an offline structural penalty derived from Forman--Ricci curvature (FRC), which captures bottleneck structures. We prove that the resulting equilibrium is well-defined, that stronger regularization reduces flow on penalized edges, and that efficiency loss depends on how closely the structural penalty approximates optimal Pigouvian tolls. Experiments on eight real-world networks under targeted and uniform demand perturbations show reduced bottleneck flow with near-optimal efficiency. FRC achieves reductions comparable to edge betweenness at substantially lower computational cost, making it a practical, robust complement to classical congestion pricing.

发表机构

• University of Southern California（南加州大学）
• California State University, Long Beach（加州州立大学长滩分校）

机构由 AI 辅助整理，请以论文原文为准。