Topic
Retrial queue
About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.
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01 Jan 2006
TL;DR: This paper shows how mean value analysis can be applied to retrial queues by illustrating the technique for the standard M/G/1 retrial queue with exponential retrial times and showing how the relations can be adapted to obtain mean performance measures in more advanced M/g/1-type ret trial queues.
Abstract: Mean value analysis is an elegant tool for determining mean performance measures in queueing models. In this paper we show how mean value analysis can be applied to retrial queues. First, we illustrate the technique for the standard M/G/1 retrial queue with exponential retrial times. After that we show how the relations can be adapted to obtain mean performance measures in more advanced M/G/1-type retrial queues.
21 citations
18 Nov 2015
TL;DR: Analysis of the sojourn time in the finite source retrial queueing system of type M/M/1//N with collision of the customers with analysis under an asymptotic condition of infinitely increasing number of sources.
Abstract: This paper deals with a finite source retrial queueing system of type M/M/1//N with collision of the customers. This means that the system has one server and N sources. Analysis of the sojourn time in the system is presented. The analysis is performed under an asymptotic condition of infinitely increasing number of sources. The approximation of the distribution of the total sojourn time in the system is derived.
21 citations
21 citations
TL;DR: In this article, an M/G/1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated.
Abstract: An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline. All customers demand the first “essential” service, whereas only some of them demand the second “optional” service, and the second service is multioptional. During the service, the server is subject to breakdown and repair. Assume that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures of interest.
21 citations
TL;DR: A discrete-time Geo/G/1 retrial queue in which all the arriving customers demand a first essential service whereas only some of them ask for a second optional service is considered, which proves the convergence to the continuous-time counterpart.
Abstract: We consider a discrete-time Geo/G/1 retrial queue in which all the arriving customers demand a first essential service whereas only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and derive a stochastic decomposition law. We also develop a recursive procedure for computing the distributions of the orbit and system size as well as the marginal distributions of the orbit size when the server is idle and busy with an essential or optional service. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.
21 citations