Scale-free resilience of real traffic jams

Significance Traffic congestion has become the most stubborn disease for the health of a city. Like the self-healing ability of a biological unit from diseases, transportation can also recover spontaneously from various disturbances. To describe this recovery, we define the resilience metric as the spatiotemporal congestion cluster, which can be used for other network systems. Based on large-scale GPS datasets, we reveal that the recovery behavior of transportation from congestion is governed by three scaling laws for all of the congestion scales. These scaling laws are found independent of microscopic details, including fluctuation of traffic demand and corresponding management. Our results of resilience scaling can help to better characterize and improve the adaptation and recovery of city traffic from various perturbations. The concept of resilience can be realized in natural and engineering systems, representing the ability of a system to adapt and recover from various disturbances. Although resilience is a critical property needed for understanding and managing the risks and collapses of transportation systems, an accepted and useful definition of resilience for urban traffic as well as its statistical property under perturbations are still missing. Here, we define city traffic resilience based on the spatiotemporal clusters of congestion in real traffic and find that the resilience follows a scale-free distribution in 2D city road networks and 1D highways with different exponents but similar exponents on different days and in different cities. The traffic resilience is also revealed to have a scaling relation between the cluster size of the spatiotemporal jam and its recovery duration independent of microscopic details. Our findings of universal traffic resilience can provide an indication toward better understanding and designing of these complex engineering systems under internal and external disturbances.