Competitive percolation strategies for network recovery

Raissa M D’Souza,Leonardo Dueñas-Osorio,Andrew M Smith,Martin Rohden,Márton Pósfai,Andrés D González

doi:10.1038/s41598-019-48036-0

Raissa M D’Souza, Leonardo Dueñas-Osorio + Show 4 more

Open Access

https://doi.org/10.1038/s41598-019-48036-0

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Abstract

Restoring operation of critical infrastructure systems after catastrophic events is an important issue, inspiring work in multiple fields, including network science, civil engineering, and operations research. We consider the problem of finding the optimal order of repairing elements in power grids and similar infrastructure. Most existing methods either only consider system network structure, potentially ignoring important features, or incorporate component level details leading to complex optimization problems with limited scalability. We aim to narrow the gap between the two approaches. Analyzing realistic recovery strategies, we identify over- and undersupply penalties of commodities as primary contributions to reconstruction cost, and we demonstrate traditional network science methods, which maximize the largest connected component, are cost inefficient. We propose a novel competitive percolation recovery model accounting for node demand and supply, and network structure. Our model well approximates realistic recovery strategies, suppressing growth of the largest connected component through a process analogous to explosive percolation. Using synthetic power grids, we investigate the effect of network characteristics on recovery process efficiency. We learn that high structural redundancy enables reduced total cost and faster recovery, however, requires more information at each recovery step. We also confirm that decentralized supply in networks generally benefits recovery efforts.

Highlights

Resilience of complex networks is one of the most studied topics of network science, with an expanding literature on spreading of failures, mitigation of damage, and recovery processes[1,2,3,4,5,6]
We have shown that recovery percolation follows our benchmark td-network design problems (NDPs) solution closely on a real-world topology
We investigated the problem of optimal cost reconstruction of critical infrastructure systems after catastrophic events

Summary

Introduction

Resilience of complex networks is one of the most studied topics of network science, with an expanding literature on spreading of failures, mitigation of damage, and recovery processes[1,2,3,4,5,6]. The goal of engineering based models of recovery is to provide system-specific predictions and actionable recommendations This is achieved by incorporating component level details and realistic transmission dynamics into the models, often in the form of generalized formulations of network design problems (NDPs), which satisfy network flows. We start by applying a generalized version of a well-studied NDP recovery algorithm[22,23,30,31] to a small case study, and we identify that the satisfaction of demand is a key driving force in the initial periods of recovery, outranking operational efficiency and direct repair costs of network elements in importance Motivated by this finding, we define a simple, competitive percolation-based model of recovery that aims to maximize the satisfaction of consumer demand in a greedy manner. We anticipate that our work can lead to efficient approximations of the NDP algorithm by leveraging the important mechanisms uncovered by our competitive percolation model

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