Robustness of interrelated traffic networks to cascading failures.

The vulnerability to real-life networks against small initial attacks has been one of outstanding challenges in the study of interrelated networks. We study cascading failures in two interrelated networks S and B composed from dependency chains and connectivity links respectively. This work proposes a realistic model for cascading failures based on the redistribution of traffic flow. We study the Barabási-Albert networks (BA) and Erdős-Rényi graphs (ER) with such structure, and found that the efficiency sharply decreases with increasing percentages of the dependency nodes for removing a node randomly. Furthermore, we study the robustness of interrelated traffic networks, especially the subway and bus network in Beijing. By analyzing different attacking strategies, we uncover that the efficiency of the city traffic system has a non-equilibrium phase transition at low capacity of the networks. This explains why the pressure of the traffic overload is relaxed by singly increasing the number of small buses during rush hours. We also found that the increment of some buses may release traffic jam caused by removing a node of the bus network randomly if the damage is limited. However, the efficiencies to transfer people flow will sharper increase when the capacity of the subway network α(S) > α0.