Stochastic Damage Models and Dependence Effects in the Survivability Analysis of Communication Networks

Stochastic analyses of the Survivability of communication networks often include a simplifying assumption that failures of, or damages to, various components of the network are statistically independent. This assumption can be quite unrealistic and can lead one to conclusions that are grossly in error. Survivability analyses and syntheses of robust networks should incorporate dependencies introduced by single events that affect large geographical areas. In this paper, we construct a stochastic damage model, analyze it, and apply the results to the survivability analysis of some simple network topologies. We demonstrate how the results can differ significantly from those obtained when independence of damage is assumed. The damage model consists of a Poisson ensemble of events (damage centers) on the plane, of given intensity (level of attack), and a network resource is damaged, and hence dysfunctional, if it lies within a radius ρ (damage radius) of some damage-causing event. Statistical properties of the damage process are obtained (e.g., the covariance function, mean and variance of the damage extent on a line resulting from the Poisson ensemble) and used to evaluate dependence effects. The damage process on a line is shown to be an alternating renewal process corresponding to the busy/idle process of an appropriately defined
M/G/\infty
queue, and standard
M/G//infty
and Type-II counter results can thus be exploited to obtain some desired quantities.