Abstract
This chapter presents a dual time-scale model of dynamic network traffic flows that integrates a day-to-day demand growth model with a differential variational inequality formulation of within-day Dynamic User Equilibrium (DUE); this model is compatible with a variety of network loading models. The differential variational inequality formulation are given for within-day DUE advantages: (1) the differential variational inequality may be very easily analyzed using the minimum principle from optimal control theory; (2) the fixed point algorithm is able to consider non-differential and non-analytic path delay operators; and (3) the rapidly growing literature on different variational inequalities will likely yield additional computational tools in the years ahead that may be exploited to find DUE flows.
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