Relative stability analysis of multiple queues

In this paper we consider a general class of single-server multiqueue systems in which the stability of any single queue can be essentially determined by the queue's arrival rate and service rate. We refer such class of systems to as Rate Stability (RS) multiqueue systems. The RS-multiqueue system is general enough to admit different stability definitions and different models. We will present two sets of new results for the RS-multiqueue systems. These results extend many previous results on the stability analysis of multiqueue systems.In the first part, we report that the RS-multiqueue systems can be classified into three classes. In each class, any pair of queues exhibits different interaction properties in three aspects: the number of intersection points of their stability boundaries, their possible relative stability relation, and whether a queue can have guaranteed service once becoming unstable.In the second part, we present a relative stability analysis of two RS-multiqueue models: a polling model and a random access model. Moreover, the analysis facilities the absolute stability analysis of the models.