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 memorandum 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 field 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 p (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 field) and used to evaluate the dependence effects on, for example, star network topologies, a communication link consisting of several repeaters, and series and parallel connection of resources. 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/a queue, and standard M/G/a and Type II counter results can thus be exploited to obtain some desired quantities.