Asymptotic-Diffusion Analysis of Multiserver Retrial Queueing System with Priority Customers

Abstract

This paper considers a priority multi-server retrial queue with two classes of customers. Primary customers have preemptive priority over secondary users. The dynamics of primary customers is the same as that of an Erlang loss system with Poisson input and exponential service time distribution. Secondary users can cognitively use the channels when they are not used by primary users. Secondary users that see all the channels occupied upon arrival join the orbit and retry later. Upon arrival, if a primary user is lost if it sees all the channels occupied by other primary users. Upon the arrival of a primary customer, if all the channels are occupied but some channels are occupied by secondary users, one of these ongoing secondary users is interrupted by the primary user and the interrupted secondary user enters the orbit. Secondary users from the orbit retry to occupy an idle server until they are successfully occupying one. For this model, we consider an asymptotic regime in which the retrial rate is extremely low. While the number of secondary users in the orbit explodes in this regime, we prove that a scaling version of the number of users in the orbit weakly converges to a diffusion process whose drift and diffusion coefficients are constructed.