The Combined Modal Split and Traffic Assignment Problem With Captive Demand in Mixed Transportation Networks

In past studies on the combined modal split and traffic assignment (CMSTA) problem, there are problems of not considering the three critical factors simultaneously: the user equilibrium (UE) on the transit network, the interaction of modes, and the captive demand. In this paper, a CMSTA model that considers the three critical factors simultaneously is presented. In the model, both the equilibrium on the auto network and the equilibrium on the transit network are considered, the interaction of the auto flow and the transit flow on link travel time is considered, and the captive demand of each mode is considered. An algorithm incorporating the double-stage algorithm, the diagonalization algorithm, and the gradient projection (GP) algorithm is presented for solving the model. The model and algorithm were applied to two networks and their validity is shown. The resultant OD demand for both modes is different with different captivity parameters. When the captivity parameter for auto is fixed, the resultant OD demand for the buses increases with the increase of the captivity parameter for the buses whereas the resultant OD demand for the autos decreases with the increase of the captivity parameter for the buses. The model applies to a city with two transportation modes: auto and bus. They are useful in the travel demand analysis and transportation planning and management.