Proof of the conjecture on the stability of a multiserver retrial queue

Abstract

In this paper we solve the conjecture made by Avram, Matei and Zhao (2014), on stability condition of an M/M/s retrial queue with Bernoulli acceptance, abandonment and feedback. The Markov process describing this queueing system is positive recurrent if rho(infinity) < 1 and transient if rho(infinity) > 1, where rho(infinity) is the traffic load under the saturation condition of the orbit. We also investigate the critical case when rho(infinity) = 1 to see if it can be either stable or unstable. (C) 2015 Elsevier B.V. All rights reserved.