A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem

Byung-Wook Wie, Roger L. Tobin, Terry L. Friesz and David Bernstein
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Byung-Wook Wie: School of Travel Industry Management, University of Hawaii, Honolulu, Hawaii 96822
Roger L. Tobin: GTE Laboratories Incorporated, Waltham, Massachusetts 02254
Terry L. Friesz: Departments of Systems Engineering and Operations Research and Engineering, George Mason University, Fairfax, Virginia 22030
David Bernstein: Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544

Transportation Science, 1995, vol. 29, issue 1, 79-92

Abstract: In this paper we formulate the dynamic network user equilibrium problem as a variational inequality problem in discrete time in terms of unit path cost functions. We then show how arc exit flow functions and nested cost operators can be used to calculate unit path costs given the departure time and route choices of network users. We also demonstrate that, assuming certain regularity conditions hold, a discrete time dynamic network user equilibrium is guaranteed to exist. Finally, a heuristic algorithm and numerical results are presented.

Date: 1995
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