A matrix continued fraction approach to multiserver retrial queues

Abstract

We consider basic M/M/c/c (c ≥ 1) retrial queues where the number of busy servers and that of customers in the orbit form a level-dependent quasi-birth-and-death (QBD) process with a special structure. Based on this structure and a matrix continued fraction approach, we develop an efficient algorithm to compute the joint stationary distribution of the numbers of busy servers and retrial customers. Through numerical experiments, we demonstrate that our algorithm works well even for M/M/c/c retrial queues with large value of c. IntroductionThis paper considers M/M/c/c retrial queues, in which if an arriving customer finds an idle server, he starts to be served, otherwise he moves to a virtual orbit, stays there for an exponentially distributed time and retries to get service. Retrial queues arise in various systems such as telecommunications, computer networks and call centers [1,6,7,21,22,27,31]. Aguir et al. [1] investigate the impact of retrials on the performance of call centers, using a fluid approximation. Artalejo and Pla [6] further evaluate the effect of customer retrials on operations of telecommunication systems, by a retrial queue with

Error Bounds for Last-Column-Block-Augmented Truncations of Block-Structured Markov Chains

“…In Section 4, we consider LD-QBDs, which describe the queue length processes in various state-dependent queues with Markovian environments, such as M/M/s retrial queues and their variants and generalizations (see, e.g., Breuer et al [10], Dudin and Klimenok [16], Phung-Duc et al [56,57]). The study of LD-QBDs and their related queueing models has been a hot topic in queueing theory for the last couple of decades (for an extensive bibliography, see Artalejo [3,4], Artalejo and Gómez-Corral [5]).…”

Multiserver Queue with Guard Channel for Priority and Retrial Customers

“…In this section, we propose a computational algorithm for the stationary distribution of our model extending that proposed by Phung-Duc et al [26] for the fundamental M/M/ / retrial queues without guard channels. In Section 5.1, we show some results which are the basis for the algorithm.…”

Algorithmic approach to Markovian multi-server retrial queues with vacations

“…The LDQBD process (2.1) with matrix components A ðnÞ ; B ðnÞ and C ðnÞ of special formula are considered by [26,28] for scalar entries and [21] for the case of matrix form entries. The approach given below for computing rate matrices is based on the method in [28] and is similar to that of [21].…”