Regrets in Routing Networks

Abstract

The impact of the recent increase in routing apps usage on road traffic remains uncertain to this day. The article introduces, for the first time, a criterion to evaluate a distance between an observed state of traffic and the user equilibrium of the traffic assignment: the average marginal regret. The average marginal regret provides a quantitative measure of the impact of routing apps on traffic using only link flows, link travel times, and travel demand. In non-atomic routing games (or static traffic assignment models), the average marginal regret is a measure of selfish drivers’ behaviors. Unlike the price of anarchy, the average marginal regret in the routing game can be computed in polynomial time without any knowledge of user equilibria and socially optimal states of traffic. First, this article demonstrates on a small example that the average marginal regret is more appropriate to define proximity between an observed state of traffic and an user equilibrium state of traffic than comparing flows, travel times, or total cost. Then, experiments on two different models of app usage and three networks (including the whole L.A. network with more than 50,000 nodes) demonstrate that the average marginal regret decreases with an increase of app usage. Sensitivity analysis of the equilibrium state with respect to the app usage ratio proves that the average marginal regret monotonically decreases to 0 with an increase of app usage. Finally, using a toy example, the article concludes that app usage could become the new Braess paradox.