An equilibrium-fixed point model for passenger assignment in congested transit networks

This paper formulates a passenger equilibrium assignment model for transit networks where it is assumed that passengers travel along the shortest hyperpaths to get to their destinations and that both the passenger waiting times and the passenger distribution between attractive lines at transit stops are flow-dependent. The resulting model is an equilibrium-fixed point model defined on the set of feasible hyperpath flow vectors and the set of feasible arc flow vectors. The paper proves the existence of at least one solution to the assignment model under useful assumptions. It also shows that the model admits a unique solution under more restrictive solution. Finally, the paper proposes a solution algorithm based on the fixed point successive approximations method.