Scalability of Network-Failure Resilience: Analysis Using Multi-Layer Probabilistic Graphical Models

In this work, we quantify scalability of network resilience upon failures. We characterize resilience as the percentage of lost traffic upon failures and define scalability as the growth rate of the percentage of lost traffic with respect to network size, link failure probability, and network traffic for given failure protection schemes. We apply probabilistic graphical models to characterize statistical dependence between physical-layer failures and the network-layer traffic, and analyze the scalability for large networks of different topologies. We first focus on the scalability of resilience for regular topologies under uniform deterministic traffic with independent and dependent link failures, with and without protection. For large networks with small probabilities of failures and without protection, we show that the scalability of network resilience grows linearly with the average route length and with the "effective" link failure probability. For large networks with 1 + 1 protection, we obtain lower and upper bound of the percentage of lost traffic. We derive approximations of the scalability for arbitrary topologies, and attain close-form analytical results for ring, star, and mesh-torus topologies. We then study network resilience under random traffic with Poisson arrivals. We find that when the network is under light load, the network resilience is reduced to that under uniform deterministic traffic. When the network load is under heavy load, the percentage of lost traffic approaches the marginal probability of link failure. Our scalability analysis shows explicitly how network resilience varies with different factors and provides insights for resilient network design.