Joint Optimization Model of Road-use Pricing and Capacity Using the Optimal Control Theory

This paper presents a joint optimization model of congested road-use pricing and capacity using the optimal control theory in disequilibrium traffic networks with elastic demand. The model aims at maximizing the total network benefit from travel within the study horizon. Referring to the discrete version of the model, the first-order optimality conditions are derived using the maximum principle and are employed to design an iterative solution method for the model. Numerical results obtained from an example network are presented to demonstrate the effectiveness of the model and the solution method.