Multi-modal traffic equilibrium model and algorithm with combined modes

A multi-modal traffic equilibrium model with combined modes is proposed. First, the super-network theory is applied to describe the traffic network with combined modes. Second, the mode and route choices are considered to be stochastic under elastic demand based on the generalized cost function. Using the network equilibrium theory, an equivalent variational inequality model is proposed after analyzing the network equilibrium conditions. Next, the existence and uniqueness of an optimal solution are given. Finally, a solution algorithm for solving the model is developed and validated by a numerical example. The influences of different parameters on Origin-Destination (OD) demand and modal split are analyzed. These results show that this model can reflect the combined travel behavior more practically and has certain generality.