Modeling Multistability and Hysteresis in Urban Congestion Spreading

TL;DR

This paper reveals that urban traffic congestion exhibits multistability and hysteresis due to hindered recovery processes, modeled through contagion-like propagation and recovery dynamics, leading to phase transitions in network states.

Contribution

It introduces a microscopic model incorporating recovery hindrance effects, explaining multistability and hysteresis in urban traffic dynamics, supported by real-world data analysis.

Findings

Congestion spreads like an epidemic but recovery is hindered by neighboring congestion.

Hindered recovery leads to discontinuous phase transitions in traffic states.

The model explains multistability and hysteresis observed in urban traffic networks.

Abstract

Growing evidence suggests that the macroscopic functional states of urban road networks exhibit multistability and hysteresis, but microscopic mechanisms underlying these phenomena remain elusive. Here, we demonstrate that in real-world road networks, the recovery process of congested roads is not spontaneous, as assumed in existing models, but is hindered by connected congested roads, and such hindered recovery can lead to the emergence of multistability and hysteresis in urban traffic dynamics. By analyzing real-world urban traffic data, we observed that congestion propagation between individual roads is well described by a simple contagion process like an epidemic, but the recovery rate of a congested road decreases drastically by the congestion of the adjacent roads unlike an epidemic. Based on this microscopic observation, we proposed a simple model of congestion propagation and dissipation, and found that our model shows a discontinuous phase transition between macroscopic functional states of road networks when the recovery hindrance is strong enough through a mean-field approach and numerical simulations. Our findings shed light on an overlooked role of recovery processes in the collective dynamics of failures in networked systems.