A Stochastic Formulation of the Optimal Boundary Control Problem Involving the Lighthill Whitham Richards Model

Abstract

It has been previously shown that the traffic control problem can be formulated as a Linear Programming (LP) problem when the corresponding initial conditions are fixed while they can be uncertain in actual control problems. This paper gives a stochastic programming formulation of the control problem, involving chance constraints to capture the uncertainty associated with the initial conditions. Different objective functions are explored using this framework and the solutions to the control problems agree well with the Monte Carlo simulation based control. To the authors’ best knowledge, this is the first time that the influence of initial condition uncertainty on traffic control is investigated through stochastic programming with chance constraints.