Optimal Control for Congestion Pricing: Theory, Simulation, and Evaluation

Abstract

This paper presents a mathematical framework for dynamic congestion pricing. The objective is to calculate an optimal toll using the optimal control theory. The problem consists of tolled lanes or routes and alternate non-tolled lanes or routes. The model is developed using a traffic conservation law, the queuing theory, and fundamental macroscopic relationships. A logit model is used for establishing the relationship between the price and the driver's choice behavior. We design a cost function and then use Hamilton–Jacobi–Bellman equation to derive an optimal control law that uses real-time information to determine an optimal tolling price. Simulations are performed to demonstrate the performance of this optimal control congestion-pricing algorithm.