Macroscopic fundamental diagram based perimeter control considering dynamic user equilibrium

Macroscopic fundamental diagram (MFD) has been receiving increasing attention recently due to its potential to describe traffic dynamics and guide the design of traffic control schemes at the network level. Perimeter control and route guidance are two main MFD-based traffic control approaches. However, current MFD-based perimeter control seldom considers travelers' route choice behavior, while MFD-based route guidance studies usually assume directly that travelers would follow the guidance and neglect the effects of traffic control. This paper aims to integrate the MFD-based perimeter control (i.e., the behavior of a system manager) and the dynamic user equilibrium based route choice behavior (i.e., the behavior of travelers) into one rigorous mathematical framework. Given a traffic network that has been divided into multiple homogeneous regions, we use MFD to describe the dynamics of each region, and use point queue model to capture the dynamics of queues formed at the boundaries. Besides, we model travelers' route choice behavior by the instantaneous dynamic user equilibrium (IDUE) principle, and design an efficient range perimeter control method from the system perspective. We model the interactions between the system manager and the travelers as a non-zero sum, non-cooperative differential game, where the system manager aims to improve the system performance while travelers try to minimize their own travel times. Meanwhile, they share the common constraints (i.e., MFD dynamics and point queue dynamics at boundaries). Mathematically, this leads to a differential complementarity system (DCS). We propose a time-stepping approach to discretize and solve the DCS model, based on which the solution existence and convergence are also established. Numerical results show that the proposed method can limit the vehicle accumulations within the efficient range of each region, which helps improve the network performance. Compared with the condition without perimeter control, the proposed control method can improve network-wide traffic performance up to 14.18%. (C) 2020 Elsevier Ltd. All rights reserved.