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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 stochastic decomposition law holds for the retrial queues under study and recursive formulas developed can be used to compute the marginal steady state probabilities of numbers of customers in the priority and non-priority groups for this case.
43 citations
TL;DR: A Markovian single server feedback retrial queue with linear retrial rate and collisions of customers is studied and the joint distribution of the server state and the orbit length under steady-state is investigated.
43 citations
TL;DR: In this article, the authors derived expressions for the expected waiting times for customers of two types who arrive in batches at a single-channel repeated orders queueing system and extended Kulkarni&s result to the case of N≧2 classes of customers.
Abstract: Kulkarni (1986) derived expressions for the expected waiting times for customers of two types who arrive in batches at a single-channel repeated orders queueing system. We propose another method of solving this problem and extend Kulkarni&s result to the case of N≧2 classes of customers.
42 citations
TL;DR: In this paper, the authors derived a stochastic decomposition law for the steady-state distribution of the number of calls in the orbit and in the system, and showed that the MIX]/Gig~1 retrial queue with Bernoulli feedback can be approximated by the corresponding discrete-time system.
Abstract: Hreceive a service of type h (h = 1, ..., H) with probability qh, where ~h=l qh 1. We study the Markov chain underlying the considered queueing system and the ergodicity condition too. We find the generating function of the number of calls in the orbit and in the system. We derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions for our queueing system and its corresponding standard system. In the special case of individual arrivals, we develop recursive formulae for calculating the steady-state distribution of the orbit size. Besides, we prove that the MIX]/Gig~1 retrial queue with Bernoulli feedback can be approximated by our corresponding discrete-time system. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics. (~) 2004 Elsevier Ltd. All rights reserved.
42 citations
TL;DR: In this article, the M|G|1 retrial queue with nonpersistent customers and orbital search is considered, and the structure of the busy period and its analysis in terms of Laplace transform is discussed.
Abstract: The M|G|1 retrial queue with nonpersistent customers and orbital search is considered. If the server is busy at the time of arrival of a primary customer, then with probability 1 − H 1 it leaves the system without service, and with probability H 1 > 0, it enters into an orbit. Similarly, if the server is occupied at the time of arrival of an orbital customer, with probability 1 − H 2, it leaves the system without service, and with probability H 2 > 0, it goes back to the orbit. Immediately after the completion of each service, the server searches for customers in the orbit with probability p > 0, and remains idle with probability 1 − p. Search time is assumed to be negligible. In the case H 2 = 1, the model is analyzed in full detail using the supplementary variable method. The joint distribution of the server state and the orbit length in steady state is studied. The structure of the busy period and its analysis in terms of Laplace transform is discussed. We also provide a direct method of calcu...
42 citations