The Peak Stability Analysis through Hysteresis Phenomenon on Heterogeneous Networks

Abstract

The macroscopic fundamental diagram (MFD) is a nonuniversal changing process over network traffic status which indicates different shapes in different networks. Hysteresis is observed in the MFD of some urban networks. It is a unique phenomenon when the network remains at low stability level and usually appears around the congestion period. This paper analyzed network peak stability through focusing on hysteresis. The formation mechanism of hysteresis is deduced from the mathematical method based on previous research studies. The precondition of hysteresis and the changing process of network state can be figured by mathematical deduction. It indicates that hysteresis only occurs conditionally in the period of macroscopic congestion and is not a universal phenomenon. Heterogeneity is an important factor leading to network instability. The hysteresis patterns of different peaks in MFD are different due to the variation of network flow. Real data are collected from Atlanta’s urban network to verify the analysis of hysteresis. To discuss the changing process of hysteresis in different peaks, a three-stage division is proposed and time series is presented as a third dimension in MFD. It is worth noticing that the existence and form of hysteresis in morning and evening peaks are different. Although there is a higher peak flow in the morning peak, the stability of the evening peak performs better when hysteresis occurs in the network. The different fluctuations in the morning and evening peaks are exhibited through the 3D version of MFD. The otherness of hysteresis in different peaks is explained through a 3D coordinate system with cross-compared corresponding indexes.