Dynamic feedback control of day-to-day traffic disequilibrium process

Abstract

In the literature, networks are usually assumed to operate at their steady states in static traffic assignment models. Given a set of demand management and supply regulation strategies, whether the vehicular traffic on a network would approach or not to a steady state under certain assumptions of behavioral realism is of importance and great interest in practice. Moreover, one primary reason for understanding the long-term traffic evolution dynamics is to control or influence the system trajectory in an efficient manner. To address these problems, we focus on a dynamic feedback control design and its subsequent steady-state analysis for a class of day-to-day (DTD) disequilibrium process so that the network traffic would evolve towards the desired stable traffic equilibrium. We propose an interconnected dynamic system framework for the stability and convergence analysis of DTD traffic adjustment process under the dynamic feedback control. Distinguished from the existing studies, we introduce a notion of output stability as well as the Lyapunov-like conditions to carry out the investigation noting that the steady states of the dynamic tolls that correspond to the Lagrange multipliers of the traffic equilibrium problem can be non-unique. The proposed method gives rise to a new approach to selecting pricing strategy. The proposed method involves only two adjustment parameters with well-identified physical meanings while the requirement on adjustment parameters for convergence and stability is mild. Finally, several numerical examples are presented to illustrate the insightful findings. It is found that, with dynamic feedback control, the network traffic state can converge to the desired equilibrium in a much faster manner than the case without control. The dynamic feedback controller can be implemented as demand management and supply regulation strategies such as road pricing and signal control.