The Anticipatory Route Guidance Problem: Formulations, Analysis and Computational Results * Jon Bottom † Soulaymane Kachani ‡ Georgia Perakis § January 2006 ¶ Abstract The anticipatory route guidance problem (ARG), an extension of the dynamic traffic user-equilibrium problem, consists of providing messages, based on forecasts of traffic conditions, to assist drivers in their path choice decisions. Guidance becomes inconsistent when the forecasts on which it is based are in- validated by drivers’ reactions to the provided messages. In this paper, we consider the problem of generating consistent anticipatory guidance that ensures that the messages based on dynamic short- est path criteria do not become self-defeating prophecies. We design a framework for the analysis of the ARG problem based on a fixed-point formulation of the problem. We also provide an infinite- dimensional variational inequality (VI) formulation. These equivalent formulations are, to the best of our knowledge, the first general analytical formulations of this problem. We establish, under weak assumptions, the existence of a solution to the ARG problem. Furthermore, we describe a solution approach based on averaging methods. Finally, we provide some computational results. 1 Introduction 1.1 Motivation An important characteristic of road traffic congestion is its randomness. Data suggest that roughly 60% of congestion-related delays on urban freeways in the U.S. are due to specific random incidents such as accidents, vehicle breakdowns and the like (see Lindley [22] for more details). Even without such incidents, congestion has a random component that derives from variability in demand patterns and in network performance. Because of this randomness, a driver’s past experience can be an unreliable basis for predicting the conditions associated with various travel options, and as a result, for making good travel choices. Advanced traveler information systems (ATIS) attempt to provide tripmakers with data intended to help them make better travel decisions. In this paper, such data will be referred to as messages. Messages may have an arbitrary content. They may be available to all tripmakers (for example by radio or television broadcasts) or only to some: for example, those who pass near a particular infrastructure (such as variable message signs or VMS) or who have special receivers in their vehicles. Tripmakers, of course, may react to the messages in any way they choose. * This paper has been made possible by a grant funded by the Region 2, University Transportation Research Center, City College of NY and the New York State Department of Transportation † Charles River Associates, Inc.; jbottom@crai.com ‡ IEOR Department, Columbia University; kachani@ieor.columbia.edu § Operations Research Center, M.I.T.; georgiap@mit.edu ¶ Preliminary version. Do not distribute without authors’ permission 1