A classified bibliography of research on retrial pueues: progress in 1990-1999
01 Dec 1999-Top (Sociedad Española de Estadística e Investigación Operativa)-Vol. 7, Iss: 2, pp 187-211
About: This article is published in Top.The article was published on 1999-12-01. It has received 314 citations till now.
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TL;DR: To limit the scope of this survey, it is decided to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.
Abstract: We have divided this review into two parts. The first part is concerned with the optimal design of queueing systems and the second part deals with the optimal control of queueing systems. The second part, which has the lion’s share of the review since it has received the most attention, focuses mainly on the modelling aspects of the problem and describes the different kinds of threshold (control) policy models available in the literature. To limit the scope of this survey, we decided to limit ourselves to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.
159 citations
TL;DR: The theory of retrial queues as discussed by the authors is a branch of the queueing theory, characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.) leaves the service area, but after some random delay returns to the system again.
Abstract: We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.) leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1 type and multiserver M/M/c type retrial queues and discuss similarities and differences between the retrial queues and their standard counterparts. We demonstrate that although retrial queues are closely connected with these standard queueing models they, however, possess unique distinguished features. We also mention some open problems.
116 citations
Cites background from "A classified bibliography of resear..."
...The interested reader may find useful material about the above variants and many other retrial models in the monograph [26], the papers [5, 7] and the references therein....
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...literature the reader is referred to the papers [5, 7, 23, 35, 50]....
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TL;DR: The main focus of this survey is to show analytic results for queue length distributions, waiting time distribution, and tail asymptotics for the queue length and waiting time distributions.
Abstract: Retrial queueing systems have been extensively studied because of their applications in telephone systems, call centers, telecommunication networks, computer systems, and in daily life. This survey deals with various retrial queueing models. The main focus of this survey is to show analytic results for queue length distributions, waiting time distributions, and tail asymptotics for the queue length and waiting time distributions. This survey also considers the stability analysis of retrial queueing models.
109 citations
TL;DR: A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed and the existence conditions for the stationary distribution are obtained and the algorithms for calculating the stationary state probabilities are elaborate.
Abstract: A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed. The continuous-time multi-dimensional Markov chain describing the behavior of the system is investigated by means of reducing it to the corresponding discrete-time multi-dimensional Markov chain. The latter belongs to the class of multi-dimensional quasi-Toeplitz Markov chains in the case of a constant retrial rate and to the class of multi-dimensional asymptotically quasi-Toeplitz Markov chains in the case of an infinitely increasing retrial rate. It allows to obtain the existence conditions for the stationary distribution and to elaborate the algorithms for calculating the stationary state probabilities.
105 citations
Cites background from "A classified bibliography of resear..."
...Good overviews of the current research on retrial queues are contained in the book of Falin and Templeton [25], the paper of Kulkarni and Liang [31] and in the recent surveys of Artalejo [4,5]....
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TL;DR: It is proved that the M/G/1 retrial queue with general retrial times can be approximated by the corresponding discrete-time system and the stochastic decomposition law is derived.
Abstract: We consider a discrete-time Geo/G/1 retrial queue in which the retrial time has a general distribution and the server, after each service completion, begins a process of search in order to find the following customer to be served. We study the Markov chain underlying the considered queueing system and its ergodicity condition. We find the generating function of the number of customers in the orbit and in the system. We derive the 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. Also, we develop recursive formulae for calculating the steady-state distribution of the orbit and system sizes. Besides, we prove that the M/G/1 retrial queue with general retrial times 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.
97 citations
Cites background from "A classified bibliography of resear..."
...For a detailed review of the main results and the literature on this topic the reader is referred to [1,2,7]....
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