Network Reliability, Performability Metrics, Rare Events and Standard Monte Carlo

In this chapter, we consider static models in network reliability, that cover a huge family of applications, going way beyond the case of networks of any kind. The analysis of these models is in general #P-complete, and Monte Carlo remains the only effective approach. We underline the interest in moving from the typical binary world where components and systems are either up or down, to a multi-variate one, where the up state is decomposed into several performance levels. This is also called a performability view of the system. The chapter then proposes a different view of Monte Carlo procedures, where instead of trying to reduce the variance of the estimators, we focus on their time complexities. This view allows a first straightforward way of exploring these metrics. The chapter focuses on the resilience, which is the expected number of pairs of nodes that are connected by at least one path in the model. We discuss the ability of the mentioned approach for quickly estimating this metric, together with variations of it. We also discuss another side effect of the sampling technique proposed in the text, the possibility of easily computing the sensitivities of these metrics with respect to the individual reliabilities of the components. We show that this can be done without a significant overhead of the procedure that estimates the resilience metric alone.