Dynamic User Equilibrium with Elastic Demand: Formulation, Qualitative Analysis and Computation

This paper is concerned with simultaneous route-and-departure choice dynamic user equilibrium with elastic travel demand (E-DUE), in which the trip matrix is determined endogenously. We present and prove an infinite-dimensional variational inequality (VI) formulation for the continuous-time E-DUE problem. An existence result for this VI is established by applying the fixed-point existence theorem (Browder, 1968) in an extended Hilbert space. Regarding computation of the E-DUE problem we present three algorithms based on the VI and differential variational inequality (DVI) formalism: a projection method (fixed-point method), a self-adaptive projection method, and a proximal point method. Rigorous convergence results are provided for these methods, which rely on increasingly relaxed notion of generalized monotonicity: mixed strongly-weakly monotonicity for the fixed-point method; pseudo monotonicity for the self-adaptive projection method, and quasi monotonicity for the proximal point method.