A Multiclass Retrial System With Coupled Orbits And Service Interruptions: Verification of Stability Conditions

Abstract

In this work, we investigate the stability conditions of a multiclass retrial system with coupled orbit queues and service interruptions. We consider a single server system accepting N classes of customers according to independent Poisson inputs and with class-dependent, arbitrarily distributed service times. An arriving customer who finds the server unavailable upon arrival, joins the corresponding orbit queue according to its class. We assume that the ?rst (oldest) blocked customer in an orbit queue attempts to connect with the server after an exponentially distributed service time, which depends both on its class, and on the current state (busy or idle) of the other orbit queues. During service times, interruptions occur according to class-dependent Poisson process, following by class-dependent arbitrarily distributed setup times. We consider both preemptive- repeat identical, and preemptive-resume interruptions. Potential applications of such a system can be found in the modelling of relay-assisted cooperative wireless networks. We focus on the non-symmetrical orbits and perform simulation experiments for the system with three classes of customers to verify stability conditions for both types of the server interruptions.

Keywords

• Multiclass retrial queues
• Stability
• Constant retrial rates
• Coupled orbit queues
• Cognitive network