On an unreliable retrial queue with general repeated attempts and J optional vacations
TL;DR: In this paper, the authors considered a single-server retrial queue with constant retrial rate and batch arrivals, in which the unreliable server has the option to take an additional vacation after the first essential vacation.
About: This article is published in Applied Mathematical Modelling.The article was published on 2016-02-15 and is currently open access. It has received 24 citations till now. The article focuses on the topics: Retrial queue & Queue.
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TL;DR: This system is analyzed as a process of quasi-birth-and-death (QBD) where the quasi-progression algorithm is applied to compute the rate matrix of QBD model, and a recursive solver algorithm for computing the stationary probabilities is developed.
49 citations
Cites background from "On an unreliable retrial queue with..."
...…other articles on unreliable retrial queues, interested researchers can refer to Atencia et al. (2008), Choudhury and Deka (2009a, 2009b), Efrosinin and Winkler (2011), Gharbi and Dutheillet (2011), Choudhury and Ke (2012, 2014), Rajadurai et al. (2014), Singh et al. (2016) and Yang et al. (2016)....
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TL;DR: The goal is to determine open service facilities and their service capacities, and to assign customers to primary and backup facilities in order to maximize an aggregated performance measure, which is a balanced sum of the customers’ and the system owner's criteria.
17 citations
TL;DR: An overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique and factors causing service interruption such as unreliable server and server vacation are presented.
Abstract: In most of the queueing models, service is considered to be complete without any interruption. But in reality, queueing systems are subject to interruptions due to failure of server or any other cause. In the present article, we present an overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique. The factors causing service interruption such as unreliable server and server vacation are elaborated. The brief of supplementary variable technique to establish the queue size distribution is explained for single server non-Markovian queueing models by incorporating the features of service interruption. The basic concepts and review of literature on the queues with server breakdown and/or vacationing server are described. The research works done during last 10 years (2010–2019) on queues with service interruption involving many other key concepts namely Bernoulli vacation, multiple vacation, bulk arrival, discouragement, etc. and queueing scenarios of service interruption are reported. Some specific applications are also highlighted.
16 citations
TL;DR: In this paper, the authors studied the operating characteristics of an M[x]/G/1 queueing system under a modified vacation policy, where the server leaves for a vacation as soon as the system is empty.
Abstract: This paper studies the operating characteristics of an M[x]/G/1 queueing system under a modified vacation policy, where the server leaves for a vacation as soon as the system is empty. The server takes at most J vacations repeatedly until at least one customer is found waiting in the queue when the server returns from a vacation. We derive the system size distribution at different points in time, as well as the waiting time distribution in the queue. Further, we derive some important characteristics including the expected length of the busy period and idle period. This shows that the results generalize those of the multiple vacation policy and the single vacation policy M[x]/G/1 queueing system. Finally, a cost model is developed to determine the optimum of J at a minimum cost. Copyright © 2006 John Wiley & Sons, Ltd.
12 citations
TL;DR: A numerical experiment illustrates the application of the results for making a decision about the rationality of establishing and maintaining a service system while an alternative system providing the same type of service already exists.
8 citations
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TL;DR: This paper presents a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process.
Abstract: In many stochastic models, particularly in queueing theory, Poisson arrivals both observe (see) a stochastic process and interact with it. In particular cases and/or under restrictive assumptions it has been shown that the fraction of arrivals that see the process in some state is equal to the fraction of time the process is in that state. In this paper, we present a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process.
1,226 citations
"On an unreliable retrial queue with..." refers background or methods in this paper
...Solving (0; ) P z from Equation (34)-(35), it finally yields after some simplification...
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...Following the Poisson Arrivals See Time Averages (PASTA) property (see Wolff, 1982), it is stated that a departing customer will see ‘j’ customers in the system just after a departure if and only if there were (j + 1) customers in the system just before the departure....
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...( ) J j j j P P z V a z p p V a z z S A z P V (35)...
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TL;DR: This survey gives an overview of some general decomposition results and the methodology used to obtain these results for two vacation models and attempts to provide a methodological overview to illustrate how the seemingly diverse mix of problems is closely related in structure and can be understood in a common framework.
Abstract: Queueing systems in which the server works on primary and secondary (vacation) customers arise in many computer, communication, production and other stochastic systems. These systems can frequently be modeled as queueing systems with vacations. In this survey, we give an overview of some general decomposition results and the methodology used to obtain these results for two vacation models. We also show how other related models can be solved in terms of the results for these basic models. We attempt to provide a methodological overview with the objective of illustrating how the seemingly diverse mix of problems is closely related in structure and can be understood in a common framework.
1,136 citations
"On an unreliable retrial queue with..." refers background in this paper
...0 1 1 0 0 (0) ( ) ( ) , P x x dx P (10)...
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...Stochastic decomposition Stochastic decomposition can be found extensively in many studies concerning M/G/1 type queueing models with server vacations (e.g., see Doshi, 1986, Takagi, 1991, Fuhrman and Cooper, 1985)....
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...A comprehensive and detailed review of the vacation models can be in Doshi (1986), Takagi (1991), Tian and Zhang (2006) and Ke et al. (2010)....
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TL;DR: In this article, the authors considered a class of M/G/1 queueing models with a server who is unavailable for occasional intervals of time and showed that the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables.
Abstract: This paper considers a class of M/G/1 queueing models with a server who is unavailable for occasional intervals of time. As has been noted by other researchers, for several specific models of this type, the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables, one of which is the stationary number of customers present in the standard M/G/1 queue i.e., the server is always available at a random point in time. In this paper we demonstrate that this type of decomposition holds, in fact, for a very general class of M/G/1 queueing models. The arguments employed are both direct and intuitive. In the course of this work, moreover, we obtain two new results that can lead to remarkable simplifications when solving complex M/G/1 queueing models.
664 citations
626 citations