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 ρ∞<1 and transient if ρ∞>1, where ρ∞ is the traffic load under the saturation condition of the orbit. We also investigate the critical case when ρ∞=1 to see if it can be either stable or unstable.