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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TL;DR: It is shown that a continuous-timeM/G/1 retrial queue can be approximated by a discrete-timeGeo/G/, and the approximation approaches the exact when the length of the interval tends to zero, and recursive formulas for the steady-state probabilities are developed.
Abstract: In this paper, we study the steady-state queue size distribution of the discrete-timeGeo/G/1 retrial queue. We derive analytic formulas for the probability generating function of the number of customers in the system in steady-state. It is shown that the stochastic decomposition law holds for theGeo/G/1 retrial queue. Recursive formulas for the steady-state probabilities are developed. Computations based on these recursive formulas are numerically stable because the recursions involve only nonnegative terms. Since the regularGeo/G/1 queue is a special case of theGeo/G/1 retrial queue, the recursive formulas can also be used to compute the steady-state queue size distribution of the regularGeo/G/1 queue. Furthermore, it is shown that a continuous-timeM/G/1 retrial queue can be approximated by a discrete-timeGeo/G/1 retrial queue by dividing the time into small intervals of equal length and the approximation approaches the exact when the length of the interval tends to zero. This relationship allows us to apply the recursive formulas derived in this paper to compute the approximate steady-state queue size distribution of the continuous-timeM/G/1 retrial queue and the regularM/G/1 queue.
68 citations
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TL;DR: This work considers a multi-server retrial queueing model in which customers arrive according to a Markovian arrival process (MAP) and performs steady state analysis of the model using direct truncation and matrix-geometric approximation.
68 citations
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TL;DR: In this article, a single-server retrial queueing system where retrial time is inversely proportional to the number of customers in the system is considered and necessary and sufficient conditions for the stability of the system are found.
Abstract: We consider a single-server retrial queueing system where retrial time is inversely proportional to the number of customers in the system. A necessary and sufficient condition for the stability of the system is found. We obtain the Laplace transform of virtual waiting time and busy period. The transient distribution of the number of customers in the system is also obtained.
65 citations
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TL;DR: This paper finds the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and shows that the results are consistent with the known results for a classical retrial queueing system.
Abstract: We consider anM/G/1 priority retrial queueing system with two types of calls which models a telephone switching system and a cellular mobile communication system. In the case that arriving calls are blocked due to the server being busy, type I calls are queued in a priority queue of finite capacityK whereas type II calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form. When λ1=0, it is shown that our results are consistent with the known results for a classical retrial queueing system.
65 citations
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TL;DR: An approximation method for the calculation of the steady-state queue size distribution is proposed and it is demonstrated through numerical results that the approximation works very well for models of practical interest.
63 citations