A model for cascading failures with the probability of failure described as a logistic function

Minjung Kim,Jun Soo Kim

doi:10.1038/s41598-021-04753-z

Abstract

In most cascading failure models in networks, overloaded nodes are assumed to fail and are removed from the network. However, this is not always the case due to network mitigation measures. Considering the effects of these mitigating measures, we propose a new cascading failure model that describes the probability that an overloaded node fails as a logistic function. By performing numerical simulations of cascading failures on Barabási and Albert (BA) scale-free networks and a real airport network, we compare the results of our model and the established model describing the probability of failure as a linear function. The simulation results show that the difference in the robustness of the two models depends on the initial load distribution and the redistribution of load. We further investigate the conditions of our new model under which the network exhibits the strongest robustness in terms of the load distribution and the network topology. We find the optimal value for the parameter of the load distribution and demonstrate that the robustness of the network improves as the average degree increases. The results regarding the optimal load distribution are verified by theoretical analysis. This work can be used to develop effective mitigation measures and design networks that are robust to cascading failure phenomena.

Highlights

In most cascading failure models in networks, overloaded nodes are assumed to fail and are removed from the network
Numerical simulations of cascading failures were performed with the probability of failure described by logistic function to investigate the robustness of the network
The parameter m of the Barabási and Albert model[23] is set to 3, obtaining the average degree k = 2m = 6

Summary

Introduction

In most cascading failure models in networks, overloaded nodes are assumed to fail and are removed from the network. This is not always the case due to network mitigation measures. Considering the effects of these mitigating measures, we propose a new cascading failure model that describes the probability that an overloaded node fails as a logistic function. In most cascading failure models, the node of a network is assumed to fail when its load exceeds its capacity. It has been argued that overloaded power lines do not immediately break down[20] In this direction, a recent study introduced the concept of the removal threshold to model the effects of mitigation measures[21]. Lj −Cj γ Cj−Cj for the linear model and as the logistic curve in Eq (4) for the logistic model

Objectives

Results

Conclusion