The Idea:Factoring in route capacities and travel costs makes traffic routing work better for each user and for the overall system.
Traffic routing is an old problem: from trains and ships to automobiles and planes to wires and cables and now to wireless networks. Both planning networks and then managing them require an understanding of how traffic will flow through them.
Jose Correa, Andreas Schulz and Nicolas Stier took a fresh look at how to make traffic routing serve both the individual user and the overall system. Previous work showed that traffic flow left on its own reaches a single equilibrium that differs in predictable ways from the best routing pattern that system managers would dictate. Yet this prior research used the simple case of a network with no limits to capacity on any route and no travel costs other than time, which traffic engineers know is never true. Based on this prior research, many experts advise that managers impose their own best routing pattern to minimize total travel time.
In contrast, this study factored in route capacities and travel costs, such as tolls, for a more realistic view of user patterns. The result is a series of equilibria, not just one, as users adjust their routes in the face of congestion and differing costs. The best of these equilibria comes quite close to the best pattern for the overall system. Users end up with equal journey times on all routes, where no single vehicle can improve its time by taking another route, and the average journey time for all users is only somewhat higher than the minimum possible when system managers dictate the flow.
This research method offers you a way to make your traffic models more realistic by factoring in route capacities and travel costs as you calculate the best of several user equilibria. Before this study, you had to choose between an unrealistic model of user equilibrium — with no route capacities or travel costs — and a top-down model of minimizing total travel time that is difficult in practice to impose on users. This study provides a formula for user equilibrium that comes close to the best results of a top-down model without the management problem of imposing a single pattern on myriad users.
Mathematics of Operations Research,
Volume: 29 | Issue: 4 | Pages: 961-76
Publication type: Journal article