A modern congestion pricing policy for urban traffic: subsidy plus toll

Bagloee, Saeed Asadi; Sarvi, Majid · 2017 · Crossref

DOI: 10.1007/s40534-017-0128-8

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Summary

This paper addresses the challenge of designing equitable and acceptable congestion pricing policies for urban traffic. While traditional tolling schemes often face public resistance due to equity concerns, and Tradable Credit Schemes (TCS) remain unimplemented due to complexity, the authors propose a Toll-and-Subsidy Scheme (TSS). This approach charges drivers on congested roads (tolls) while rewarding those who use underutilized alternative routes (subsidies). The primary research question is determining the optimal toll and subsidy values for a set of roads with capped traffic volumes to achieve a specific traffic distribution. The study formulates the problem as a Capacitated Traffic Assignment Problem (CTAP). The authors employ a solution method that interprets the Lagrange multipliers of the capacity constraints as the toll or subsidy values. By relaxing the non-negativity constraint of toll values, the method allows for subsidies (negative tolls). The CTAP is transformed into an un-capacitated Traffic Assignment Problem (TAP) by augmenting the travel time of roads with these Lagrangian values, effectively inflating the cost of oversaturated roads until traffic volumes stabilize at their target capacities. This iterative heuristic avoids the computational complexity of bilevel programming often associated with second-best congestion pricing. The methodology is validated using a real dataset from Winnipeg, Canada, serving as a pilot study for large-sized networks. The results demonstrate that the proposed method successfully computes valid toll and subsidy sets that enforce traffic volumes below target rates. The authors highlight that computational time is a significant factor, but their approach is affordable and scalable because it bounds traffic volumes from above and avoids the infeasibility issues associated with strict revenue-neutral constraints. The study proves that a solution always exists if the total toll revenue exceeds the total subsidy payout, ensuring the scheme is Pareto-improving. The interpretation of Lagrangian values provides a direct mathematical link between capacity constraints and pricing mechanisms, offering a clear policy tool for authorities. The significance of this work lies in its contribution to the practical implementation of congestion pricing. By introducing subsidies alongside tolls, the TSS enhances equity and public acceptability, addressing key barriers to adoption. The method offers a computationally efficient alternative to complex tradable credit systems, providing traffic authorities with a robust tool to manage congestion by redistributing traffic loads across the network. The findings suggest that relaxing revenue-neutral constraints can secure feasible solutions that improve system efficiency without making any commuter worse off, thereby supporting the broader goal of achieving system-optimal traffic patterns.

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