Optimal and robust strategies for freeway traffic management under demand and supply uncertainties: an overview and general theory

Abstract

This paper investigates optimal decision-making for traffic management under demand and supply uncertainties by stochastic dynamic programming. Traffic flow dynamics under demand and supply uncertainties is described by a simplified version of the stochastic cell transmission model. Based on this model, the optimal traffic management problem is analysed wherein the existence of solution is guaranteed by verifying the well-posed condition. An analytical optimal control law is derived in terms of a set of coupled generalised recursive Riccati equations. As optimal control laws may be fragile with respect to model misspecification, a robust (optimal) decision-making law that aims to act robust with respect to the parameter misspecification in the traffic flow model (which can be originated from model calibration), and to attenuate the effect of disturbances in freeway networks (wherein demand uncertainty is usually regarded as a kind of disturbance) is proposed. Conventionally, network uncertainties have been considered to induce negative effects on traffic management in transportation literature. In contrast, the proposed methodology outlines an interesting issue that is to make benefit (or trade-off) from the inherent network uncertainties. Finally, some practical issues in traffic management that can be addressed by extending the current framework are briefly discussed.