Road traffic networks: Optimal transport and incentives

In this paper we analyze the effectiveness of incentives in reducing highway congestion by shifting some commuters to travel in the off-peak hour. We develop a model for the reduction of transport capacity due to congestion in a highway segment, building on previous work. Under this model, the “waiting time” of a commuter is taken to be equal to their actual commuting time less the time needed to traverse the highway segment under free flow. We wish to minimize the “cost of congestion”, which is equal to the sum of the waiting times of all commuters, by incentivizing some commuters to shift from the peak hour. We find that the cost of congestion is intimately related to the Wasserstein distance of optimal transport theory. Further, we find that the cost of congestion is a convex function of the arrival rate distribution. We then formulate a model for the cost of shifting user arrival times to obtain a new arrival time distribution with lower congestion. Using an example, we shall illustrate the benefits of shifting commuter behavior to reduce peak hour traffic congestion.