Fault Tolerance Metrics Research Articles

Markov Chains for Fault-Tolerance Modeling of Stochastic Networks

Most real-world networks are time-varying, and many are subject to the stochastic functioning of their nodes and edges. Examples can be seen in the human brain undergoing an epileptic seizure, spontaneous infection and recovery in epidemics, and intermittent functioning of devices in the Internet of Things. Moreover, such networks are becoming increasingly large due to rapid technological advances. However, little has been done to study time-varying, large-scale, stochastic networks (SNs) from a reliability engineering perspective. Toward this goal, this article develops a fault-tolerance model for a type of time-varying network in which nodes (and/or edges) stochastically switch between active and inactive states. It considers fault tolerance from a global connectivity point of view, which has applications in many natural and engineered networks. Specifically, this article presents a Markov chain framework that models the dynamic behavior of nodes and allows for the computation of quantitative measures, including availability and time-to-failure metrics. To accommodate large-scale networks and emphasize global connectivity, this framework utilizes percolation theory, which has recently been of interest in the reliability engineering discipline, to characterize network failure. This article makes several contributions: it proposes a Markov chain framework for computing fault-tolerance metrics that is tractable for large-scale networks, it shows the existence of a phase transition in network availability of a time-varying SN, and it accounts for finite-size effects of percolation in the fault-tolerance model. The proposed methodology is applied to Erdös–Rényi random graphs and a real, large-scale power grid. Experimental results provide insights into network design, maintenance, and failure prevention of time-varying SNs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work develops a fault-tolerance model for time-varying stochastic networks in which nodes (and/or edges) randomly switch between active and inactive states. To address increasingly large-scale networks that are being studied, this article appeals to percolation theory. Fault tolerance is, thus, studied from a global connectivity perspective where the existence of a large connected component containing most of the nodes characterizes the functioning of the network. Specifically, this article presents a continuous-time Markov chain (CTMC) framework that models node dynamics and allows for the computation of fault-tolerance metrics, including network availability and mean time to failure. The proposed framework computes metrics efficiently for large networks and allows for studying their asymptotics. The percolation threshold describing the dissolution of the large connected component is used as the failure criterion in the CTMC. The practitioner should note that several assumptions are made in the proposed CTMC framework: nodes possess identical and time-invariant failure and recovery rates, node failure and recovery times are exponentially distributed, and node dynamics are independent of one another. In addition, fault-tolerance metrics computed for finite networks are estimators of the true metric values. The proposed framework is advantageous for quantifying the fault tolerance of large-scale, time-varying networks where the combinatorial explosion and a changing network topology pose challenges to the use of traditional reliability methods. A case study of a power grid network shows how to apply the proposed methodology to real networks.

A topology control algorithm based on D-region fault tolerance

In a wireless network, node failure due to either natural disasters or human intervention can cause network partitioning and other communication problems. For this reason, a wireless network should be fault tolerant. At present, most researchers use k-connectivity to measure fault tolerance, which requires the network to be connected after the failure of any up to k-1 nodes. However, wireless network node failures are usually spatially related, and particularly in military applications, nodes from the same limited area can fail together. As a metric of fault-tolerance, k-connectivity fails to capture the spatial relativity of faults and hardly satisfies the fault tolerance requirements of a wireless network design. In this paper, a new metric of fault-tolerance, termed D-region fault tolerance, is introduced to measure wireless network fault tolerance. A D-region fault tolerant network means that even after all the nodes have failed in a circular region with diameter D, it still remains connected. Based on D-region fault tolerance, we propose two fault-tolerant topology control algorithms—the global region fault tolerance algorithm (GRFT) and the localized region fault tolerance algorithm (LRFT). It is theoretically proven that both algorithms are able to generate a network with D-region fault tolerance. Simulation results indicate that with the same fault tolerance capabilities, networks based on both GRFT and LRFT algorithms have a lower transmission radius and lower logical degree.