Resilient perimeter control for hyper-congested two-region networks with MFD dynamics

Understanding the resilience of transportation networks has received considerable research attention. Nevertheless in the field of network traffic flow control, few control approaches target the mitigation from hyper-congestion, and the control objective has rarely touched the system resilience requirement which focuses on system recovering from hyper-congested state. This paper sheds light on a resilience-oriented network control. We firstly define the traffic resilience as the integral of deviation against optimal state from disturbance generation moment t₀ to recovery moment t_f. Then, we propose a control method under hyper-congested situations by formulating the analytical problem using a two-reservoir transportation system with parabola-shaped Macroscopic Fundamental Diagrams (MFDs), using phase diagram analysis, attraction region derivation and switched controller design. Afterwards, we evaluate the system resilience performances between two classic perimeter control schemes (constant perimeter control (CPC) and state-feedback control (SFC)) and the proposed resilient control scheme. Results show that proposed controller can ensure the system to recover from hyper-congestion to the optimal state while existing studies failed to recover. This resilience is confirmed in various case study scenarios, e.g., when the level of hyper-congestion is different. More promisingly, the proposed control shows high compatibility with the form of the MFDs, e.g., the recover can be achieved under hysteresis conditions which are common for network-level traffic dynamics. These findings will help to design an intelligent transportation system with enhanced resilience.