Approximately Optimal Toll Design for Efficiency and Equity in Arc-Based Traffic Assignment Models

Congestion pricing policies have emerged as promising traffic management tools to alleviate traffic congestion caused by travelers' selfish routing behaviors. The core principle behind deploying tolls is to impose monetary costs on frequently overcrowded routes, to incentivize self-interested travelers to select less easily congested routes. Recent literature has focused on toll design based on arc-based traffic assignment models (TAMs), which characterize commuters as traveling through a traffic network by successively selecting an outgoing arc from every intermediate node along their journey. However, existing tolling mechanisms predicated on arc-based TAMs often target the design of a single congestion-minimizing toll, ignoring crucial fairness considerations, such as the financial impact of high congestion fees on low-income travelers. To address these shortcomings, in this paper, we pose the dual considerations of efficiency and equity in traffic routing as bilevel optimization problems. Since such problems are in general computationally intractable to solve precisely, we construct a linear program approximation by introducing a polytope approximation for the set of all tolls that induce congestion-minimizing traffic flow patterns. Finally, we provide numerical results that validate our theoretical conclusions.