A Simulation-Based Dynamic Intermodal Network Equilibrium Algorithm

This paper introduces a Variational Inequality (VI) formulation for the time-dependent combined mode split and traffic assignment problem. Travel costs are represented by generalized cost functions and mode choices are deterministically obtained based on assignment to intermodal least cost paths without accounting for possible randomness in travelers' choices. The intermodal user equilibrium (IUE) is estimated using an inner approximation (IA) algorithm that results in a nonlinear program with linear constraints. The algorithm converges assuming continuous and monotonic path travel cost functions. The paths on multimodal networks are computed with an intermodal optimum path algorithm; a cell transmission-based simulator, enhanced to account for both automobile and transit vehicles, is used to estimate the path travel costs. A heuristic search approach is proposed and implemented in the VISTA simulation-based framework. Computational results are presented on example networks to test convergence and equilibrium.