Optimal utilization of a transport system with auto/transit parallel modes

In this paper, an optimal utilization model of a congested transport system with auto/transit parallel modes is formulated using optimal control theory. The model aims at maximizing the net economic benefit over the whole study horizon of time. It is shown that at equilibrium, the mode choice at aggregate demand level is governed by a multinomial exponential function, while for each mode, the generalized costs for all departure times that are actually used are identical. The generalized costs include the optimal variable fares and tolls imposed on transit mode and auto mode commuters, respectively; this transport pricing supports the system optimum as a user equilibrium. An iterative discrete time algorithm using the augmented Lagrangian method is proposed and illustrated with a numerical example.