Stability Conditions for Multidimensional Queueing Systems with Computer Applications

A fundamental question arising in the analysis of queueing systems is whether a system is stable or unstable. For systems modeled by infinite Markov chains, we may study the ergodicity and nonergodicity of the chains. Foster showed that sufficient conditions for ergodicity are linked with the average drift. However, complications arise when multidimensional Markov chains are analyzed. We present three methods that provide 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.