Networks and Spatial Economics, 5: (2005) 71–87  C 2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands. Some Consistency Conditions for Dynamic Traffic Assignment Problems H.M. ZHANG ∗ XIAOJIAN NIE Department of Civil and Environmental Engineering University of California, Davis, CA 95616, USA email: hmzhang@ucdavis.edu Abstract This paper explores some critical issues in modeling network traffic flow for predictive user optimal dynamic traffic assignment. They include the role of FIFO (first-in-first-out) in link, path and network traffic dynamics, minimal set representation of link traffic evolution, and consistency conditions for link models. It is found that (1) link FIFO plays a central role in modeling link, path and network traffic flow evolution, and (2) the dimension of a minimal state set that adequately describes link traffic flow under FIFO is two. Moreover, two sufficient FIFO conditions are provided, and pitfalls in using these conditions to enforce FIFO are pointed out. Finally, ramifications of these findings to DTA modeling are also discussed. Keywords: Dynamic traffic assignment, link traffic flow models, FIFO, consistency conditions 1. Introduction The problem of assigning time-dependent Origin-Destination (O-D) trip demands to a road network—the so-called dynamic traffic assignment (DTA) problem—has been actively re- searched since the first DTA model was formulated and solved by Merchant and Nemha¨ user (1978a, b). Out of this research activity emerges four strands of DTA formulations: for- mulations based on mathematical programming methods (e.g., Janson, 1991), formulations based on optimal control theory (e.g., Friesz et al., 1989), formulations based on variational inequalities (e.g., Nagurney, 1993; Friesz et al., 1993; Ran and Boyce, 1996; Lo, 1999), and formulations based on computer simulations (e.g., Mahmassani et al., 1992; Smith, 1993; Tong and Wong, 2000). Despite a variety of differences in these formulations, all of them share three basic elements that are essential to any DTA model: (1) user behavior, (2) flow conservation, and (3) traffic evolution. User behavior specifies the rules on which a traveler chooses his route of travel (here we are solely concerned with the fixed time-dependent demand case). Different formulations may differ in their behavioral assumptions, of which three kinds are common—that of system optimal (SO-DTA), that of reactive user optimal (RUO-DTA) and that of predictive user optimal (PUO-DTA). In a SO-DTA model, users are supposed to choose a route so as to minimize the overall system travel cost; in a RUO-DTA model a user behaves myopically, that is, he chooses at any time instant t the minimal cost ∗ Corresponding author.