Exact analysis of a class of GI/G/1-type performability models

We present an exact decomposition algorithm for the analysis of Markov chains with a GI/G/1-type repetitive structure. Such processes exhibit both M/G/1-type & GI/M/1-type patterns, and cannot be solved using existing techniques. Markov chains with a GI/G/1 pattern result when modeling open systems which accept jobs from multiple exogenous sources, and are subject to failures & repairs; a single failure can empty the system of jobs, while a single batch arrival can add many jobs to the system. Our method provides exact computation of the stationary probabilities, which can then be used to obtain performance measures such as the average queue length or any of its higher moments, as well as the probability of the system being in various failure states, thus performability measures. We formulate the conditions under which our approach is applicable, and illustrate it via the performability analysis of a parallel computer system.