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Journals ACM SIGMETRICS Performance Evaluation Review Volume 31 Issue 2

We present an aggregation-based algorithm for the exact analysis of Markov chains with GI/G/1-type pattern in their repetitive structure, i.e., chains that exhibit both M/G/1-type and GI/M/1-type patterns and cannot be solved with existing techniques. Markov chains with a GI/G/1 pattern result when modeling open systems with faults/repairs that accept jobs from multiple exogenous sources. Our method provides exact computation of the steady state probabilities, and allows computation of performance measures of interest including the system queue length or any of its higher moments, the exact probability of system failures and repairs, and consequently a host of performability measures. Our algorithm also applies to systems that are purely of the M/G/1-type or the GI/M/1-type, or their intersection, i.e., quasi-birth-death processes.

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An aggregation-based method for the exact analysis of a class of GI/G/1-type processes

Riska, Alma; Smirni, Evgenia; Ciardo, Gianfranco
ACM SIGMETRICS Performance Evaluation Review , Volume 31 (2)
Association for Computing Machinery – Sep 1, 2003

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