USER-EQUILIBRIUM PROPERTIES OF FIXED-POINTS IN DYNAMIC TRAFFIC ASSIGNMENT

This paper considers the problem of dynamic traffic assignment under t he principle that individual drivers will choose fastest paths, in the dynamic situation where path durations consist of time-dependent link travel times. Rather than constructing a unified model encompassing t raffic dynamics and route choice, we decompose the model into an assig nment mapping, which identifies the link travel times resulting from a n input routing policy, and a routing mapping, which yields fastest-pa th routings associated with input link travel times. Since time-dynami c link travel times are influenced by route choice, this dynamic situa tion therefore encompasses predictive routing strategies. We establish that user-equilibrium routing policies are fixed points of the compos ition of the routing and assignment functions. After discussing diffic ulties associated with establishing existence of fixed points under di screte-time modeling and all-or-nothing routing, we present instead ne w iterative routing mappings for continuous-time multipath routing (th e splitting of a single-class flow onto multiple paths), which adjust routing policies more incrementally. We provide sufficient conditions for existence of fixed points in various routing policy domains and of fer some suggestions on the computation of these fixed-point policies. (C) 1998 Elsevier Science Ltd. All rights reserved.