Macroscopic and Microscopic Characteristics of Networks with Time-variant Functionality for Evaluating Resilience to External Perturbations

TL;DR

This paper introduces new measures to evaluate the resilience of networks considering both their structure and functionality over time, demonstrated through traffic network analysis during Hurricane Harvey.

Contribution

It proposes three novel indices and an integrated resilience metric that jointly assess macroscopic, microscopic, and temporal network resilience aspects.

Findings

Link weights and node degrees follow a scale-free distribution during flooding.

The measures effectively capture resilience curves and link irregularities.

Insights suggest ways to improve network resilience against external shocks.

Abstract

Knowledge of time-variant functionality of real-world physical, social, and engineered networks is critical to the understanding of the resilience of networks facing external perturbations. The majority of existing studies, however, focus only on the topological properties of networks for resilience assessment, which does not fully capture their dynamical resilience. In this study, we evaluate and quantify network resilience based both on the functionality states of links and on topology. We propose three independent measures---the failure scaling index (FSI), the weighted degree scaling index (WDSI), and the link functionality irregularity index (LFII)---that capture macroscopic, microscopic, and temporal performance characteristics of networks. Accordingly, an integrated general resilience (GR) metric is used to assess performance loss and recovery speed in networks with time-variant functionality. We test the proposed methods in the study of traffic networks under urban flooding impacts in the context of Harris County, Texas, during Hurricane Harvey using a high-resolution dataset, which contains temporal speed of 20,000 roads every 5 minutes for 5 months. Our results show that link weights and node weighted degrees with perturbed functionality in the traffic network during flooding follow a scale-free distribution. Hence, three proposed measures capture clear resilience curves of the network as well as identify the irregularity of links. Accordingly, network performance measures and the methodology for resilience quantification reveal insights into the extent of network performance loss and recovery speed, suggesting possible improvements in network resilience in the face of external perturbations such as urban flooding.