Ultimate Stability Conditions for Some Multidimensional Distributed Systems
Wojciech Szpankowski, Vernon J. Rego · Purdue e-Pubs (Purdue University System) · 1987
Multidimensional systems with dependent components are useful representations for processes of interest in the fields of computer science and computer comnnmications.Such systems can function properly if and only if they are stable.Until now, the question of ascertaining the stability of such systems in general has been often open, mainly due to difficulties with dependence and non-Marimvian behaviour.In this paper we derive very general stability conditions for a class of distributed systems.These criteria say, as expected, that the average input rate cannol exceed a so called modified service rate, introduced in the paper, in order to assure stability of the system.The main results are applied to systems such as token passing rings, coupledprocessor systems, buffered ALOHA systems with slotted and unslotted channels.and buffered multiaccess systems with conflict resolution algorithms.