Schedule-based transit assignment model with travel strategies and capacity constraints

In this paper, we propose a user equilibrium transit assignment model that takes into account transit schedules and individual vehicle capacities explicitly. The model assumes that passengers use travel strategies that can be adaptive over time and graphically represented as subgraphs. When loading a vehicle, on-board passengers continuing to the next stop have priority and waiting passengers can be loaded on a first-come-first-serve basis or in a random manner. The latter is appropriate when passengers mingle on waiting platforms. When a vehicle is full, passengers unable to board must wait for the next vehicle to arrive. The equilibrium conditions can be stated as a variational inequality involving a vector-valued function of expected strategy costs. Although the function is not necessarily continuous or monotonic, a solution to the variational inequality exists. To find a solution, we propose a method that takes successive averages as its iterates and generates strategies during each iteration by solving a dynamic program. Numerical examples empirically demonstrate that the algorithm converges to an equilibrium solution.