Recovery of Interdependent Networks

TL;DR

This paper proposes a recovery strategy for interdependent networks facing cascading failures, demonstrating through analysis and simulations that effective recovery probabilities can prevent total system collapse.

Contribution

It introduces a practical node recovery method for interdependent networks and characterizes the phase transitions between collapse and recovery.

Findings

A critical recovery probability exists that prevents system collapse.

Three distinct phases identified in the recovery and failure dynamics.

Recovery strategy can fully restore the system if the probability exceeds a threshold.

Abstract

Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy of nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery $\gamma$, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction $1-p$ of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane $\gamma-p$ of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot avoid the system collapse.