Stability Conditions for Multidimensional Queueing Systems and Applications to Analysis of Computer Systems

A fundamental question arising in queueing system analysis is whether a system is stable or unstable. For systems modelled by infinite Markov chain, we may study ergodicity and nonergodicity of the chains. Foster [6] showed that sufficient conditions for ergodicity are linked with the average drift, however. complications arise when multidimensional Markov chains are analysed. We shall present three methods providing sufficient conditions for ergodicity and nonergodicity of a multidimensional ~mrkov chain. These methods are next applied to two multidimensional queueing systems: buffered contention packet broadcast system and coupled-processor system.

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