Towards Computable Stability Criteria for Some Multidimensional Stochastic Processes Arising in Queueing Models

Primary motivation for this research is the need for firmly based but also easily computable methods applicable to the study of stability of stochastic models arising in lhe analysis of computer and communication systems. The stability definition adopted in this work is broad enough to cover such problems as existence of stationary distribution, ergodicity and nonergodi-city, finiteness of some quantities of interest and so forth. In this article, though we mainly discuss multidimensional Markovian models. the stability of such models is ascertained by Marko-vian and non-Markovian melhods. In the first category, we concenttate on the Lyapunov (test) function approach. The latter methodology is based. on Loynes' result regarding stability of a general (non-Markovian) GIGII queue. A variety of approaches are used to obtain ultimate stability conditions for practical systems such as token passing rings, coupled-processor systems. buffered ALOHA systems and a decentralized dynamic control protocol for broadcast communications .