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Unformatted text preview: SYSTEM-OPTIMAL ROUTING OF TRAFFIC FLOWS WITH USER CONSTRAINTS IN NETWORKS WITH CONGESTION OLAF JAHN , ROLF H. MOHRING , ANDREAS S. SCHULZ , AND NICOLAS E. STIER MOSES Abstract. The design of route guidance systems faces a well-known dilemma. The approach that theoretically yields the system-optimal trac pattern may discriminate against some users in favor of others. Proposed alternate models, however, do not directly address the system perspective and may result in inferior performance. We propose a novel model and corresponding algorithms to resolve this dilemma. We present computational results on real-world instances and compare the new approach with the well-established trac assignment model. The essence of this study is that system-optimal routing of trac ow with explicit integration of user constraints leads to a better performance than the user equilibrium, while simultaneously guaranteeing superior fairness compared to the pure system optimum. 1. Introduction Route guidance and information systems are designed to assist drivers in making route decisions. Such devices can provide information (e.g., about conditions drivers are likely to experience) or give recommendations (e.g., leave the highway at the next exit and turn right). We will concentrate on in-vehicle route guidance devices that provide recommendations to drivers. Drivers enter their destinations at the beginning of the trip, and the system computes routes based on digital maps, up- to-date trac data and current vehicle positions determined with the help of the Global Positioning System (Henry, Charbonnier, and Farges 1991). These devices normally use visual and acoustic indicators to aid drivers in following the proposed route. Currently, many cars are already equipped with simple versions of these devices, and with prices going down many more are likely to have one in the not-so-distant future. For that reason, it is widely hoped that route guidance systems can help to alleviate congestion caused by the still increasing amount of road trac. Even small improvements can have a significant impact given that the congestion bill in the U.S. alone was $67.5 billion in the year 2000, consisting of 3.6 billion hours of delay plus 5.7 billion gallons of gas (Texas Transportation Institute 2002). Several kinds of in-car navigation systems have been proposed. The simplest devices perform static guidance; i.e., they work with information that is infrequently updated. Most of the in-car guidance consoles deployed today are of this type. Their main goal is to provide information to drivers who do not know the area well. From an algorithmic point of view, they are straightforward: they only compute shortest paths (or approximations thereof) to the destinations with respect to Date : November 2002; revised December 2003....
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- Spring '04