Demand-Independent Optimal Tolls

TL;DR

This paper explores the existence of demand-independent tolls in congestion networks that can induce optimal flow regardless of demand, characterizing their conditions based on network and cost structures.

Contribution

It provides necessary and sufficient conditions for demand-independent optimal tolls, including specific cost functions and network topologies, expanding understanding of toll design.

Findings

Demand-independent tolls exist if edge costs are shifted monomials.

Non-negative demand-independent tolls exist in directed acyclic graphs.

Networks with a single OD pair admit tolls satisfying budget constraints.

Abstract

Wardrop equilibria in nonatomic congestion games are in general inefficient as they do not induce an optimal flow that minimizes the total travel time. Network tolls are a prominent and popular way to induce an optimum flow in equilibrium. The classical approach to find such tolls is marginal cost pricing which requires the exact knowledge of the demand on the network. In this paper, we investigate under which conditions demand-independent optimum tolls exist that induce the system optimum flow for any travel demand in the network. We give several characterizations for the existence of such tolls both in terms of the cost structure and the network structure of the game. Specifically we show that demand-independent optimum tolls exist if and only if the edge cost functions are shifted monomials as used by the Bureau of Public Roads. Moreover, non-negative demand-independent optimum tolls exist when the network is a directed acyclic multi-graph. Finally, we show that any network with a single origin-destination pair admits demand-independent optimum tolls that, although not necessarily non-negative, satisfy a budget constraint.