Retrial queue

About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.

Tail asymptotics for M/M/c retrial queues with non-persistent customers

Abstract: In this paper, we consider a variant of the classical M/M/c retrial queue, in which we allow non-persistent customers. When c > 1, this system does not have an explicit closed form solution for the joint stationary distribution of the number of retrial customers in the orbit and the number of busy servers. Our main focus is on the tail asymptotics for the joint probabilities. We first present a matrix-product solution for the joint stationary probability vectors, which is further simplified to a scalar-product form, according to matrix-analytic theory. We then apply the censoring technique, which has been proven an efficient approach for analyzing queueing systems including retrial queues, to obtain the censored equations and the Key Lemma. In terms of these results, we finally prove an exact tail asymptotic result for the stationary probabilities.

Matrix analytical methods for M/PH/1 retrial queues

Abstract: A matrix analytical approach is applied to retrial queues with phase type service time distributions. A matrix product form is obtained for the joint stationary distribution of queue length and service phase and a stability condition is derived. A numerical method is derived for obtaining the distribution of the number of retrials per customer and the distribution and moments of the waiting time in orbit. We also consider two extensions: The M/M/1 retrial queue with geometric loss and state dependent M/PH/1 retrial queues.

Performance Analysis of a Two-Server Heterogeneous Retrial Queue with Threshold Policy

Abstract: In the paper we deal with a Markovian queueing system with two heterogeneous servers and constant retrial rate. The system operates under a threshold policy which prescribes the activation of the faster server whenever it is idle and a customer tries to occupy it. The slower server can be activated only when the number of waiting customers exceeds a threshold level. The dynamic behaviour of the system is described by a two-dimensional Markov process that can be seen as a quasi-birth-and-death process with infinitesimal matrix depending on the threshold. Using a matrix-geometric approach we perform a stationary analysis of the system and derive expressions for the Laplace transforms of the waiting time as well as arbitrary moments. Illustrative numerical results are presented for the threshold policy that minimizes the mean number of customers in the system and are compared with other heuristic control policies.