Stability Analysis of a Multiclass Retrial System with Coupled Orbit Queues

Abstract

In this work we consider a single-server system accepting N types of retrial customers, which arrive according to independent Poisson streams. In case of blocking, type-i customer, \(i=1,2,...,N\) is routed to a separate type-i orbit queue of infinite capacity. Customers from the orbit queues try to access the server according to the constant retrial policy. We consider coupled orbit queues. More precisely, the orbit queue i retransmits a blocked customer of type-i to the main service station after an exponentially distributed time with rate \(\mu _{i}\), when at least one other orbit queue is non-empty. Otherwise, if all other orbit queues are empty, the orbit queue i changes its retransmission rate from \(\mu _{i}\) to \(\mu _{i}^{*}\). Such a scheme arises in the modeling of cooperative cognitive wireless networks, in which a node is aware of the status of other nodes, and accordingly, adjusts its retransmission parameters in order to exploit the idle periods of the other nodes. Using the regenerative approach we obtain the necessary conditions of the ergodicity of our system, and show that these conditions have a clear probabilistic interpretation. We also suggest a sufficient stability condition. Simulation experiments show that the obtained conditions delimit the stability domain with remarkable accuracy.