Modeling multistability and hysteresis in urban congestion spreading

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 congestion dynamics. By analyzing real-world urban traffic data, we observed that congestion propagation between individual roads is well described by a simple contagion process as 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.