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Stability conditions for multidimensional queueing systems with computer applications. (English) Zbl 0666.60068

A fundamental question arising in the analysis of queueing systems is whether a system is stable or unstable. For systems modelled by infinite Markov chains, we may study ergodicity and nonergodicity of the chains. F. G. Foster [Ann. Math. Statistics 24, 355-360 (1953; Zbl 0051.106)] showed that sufficient conditions for ergodicity are linked with the average drift. However, complications arise when multidimensional Markov chains are analyzed.

We shall present three methods providing sufficient conditions for ergodicity and nonergodicity of a multidimensional Markov chain. These methods are next applied to two multidimensional queueing systems: buffered contention packet broadcast systems and coupled-processor systems.

Reviewer: W.Szpankowski
60J20Applications of Markov chains and discrete-time Markov processes on general state spaces
60K25Queueing theory
68M20Performance evaluation of computer systems; queueing; scheduling