Discrete-Time Geox/G/1 Retrial Queue with General Retrial Times, Working Vacations and Vacation Interruption

doi:10.1080/16843703.2013.11673427

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Discrete-Time Geox/G/1 Retrial Queue with General Retrial Times, Working Vacations and Vacation Interruption

Journal Article•DOI•

Discrete-Time Geox/G/1 Retrial Queue with General Retrial Times, Working Vacations and Vacation Interruption

Shan Gao¹, Jinting Wang¹•Institutions (1)

Beijing Jiaotong University¹

01 Jan 2013-Quality Technology and Quantitative Management (Taylor & Francis)-Vol. 10, Iss: 4, pp 495-512

TL;DR: In this article, a discrete-time 1 X Geo G retrial queue with general retrial times was considered, and working vacations and vacation interruption policy was introduced into the retrial queuing.

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Abstract: We consider a discrete-time 1 X Geo G retrial queue with general retrial times, and introduce working vacations and vacation interruption policy into the retrial queue. Firstly, we analyze the stationary condition for the embedded Markov chain at the departure epochs. Secondly, using supplementary variable method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, some numerical examples are presented.

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Journal Article•DOI•

A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process

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Baoliang Liu¹, Lirong Cui², Yanqing Wen¹, Jingyuan Shen²•Institutions (2)

Shanxi Datong University¹, Beijing Institute of Technology²

01 Oct 2015-Reliability Engineering & System Safety

TL;DR: This paper studies a cold standby repairable system with working vacations and vacation interruptions, and builds a vector-valued Markov process constructed for this system using the matrix-analytic method.

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42 citations

Journal Article•DOI•

Analysis of a single server batch arrival unreliable queue with balking and general retrial time

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Djamila Zirem¹, Mohamed Boualem¹, Karima Adel-Aissanou¹, Djamil Aïssani¹•Institutions (1)

University of Béjaïa¹

02 Nov 2019-Quality Technology and Quantitative Management

TL;DR: This model has a potential applications in various fields, such as in the cognitive radio network and the manufacturing systems, and some important performance measures, stochastic decomposition property of the system size distribution and the reliability indices are obtained.

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Abstract: This paper deals with a batch arrivals queue with general retrial time, breakdowns, repairs and reserved time Here we assume that customers arrive according to compound Poisson processes Any arri

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21 citations

Journal Article•DOI•

An M/G/1 retrial queue with balking customers and Bernoulli working vacation interruption

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Tao Li¹, Liyuan Zhang¹, Shan Gao•Institutions (1)

Shandong University of Technology¹

03 Sep 2019-Quality Technology and Quantitative Management

TL;DR: By applying the supplementary variable technique, the steady state joint distribution of the server and the number of customers in the orbit is obtained and various interesting performance measures are derived.

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Abstract: In this paper, an M/G/1 retrial queue with general retrial times and Bernoulli working vacation interruption is considered. If the server is busy, an arriving customer either enters an orbit with p...

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15 citations

Cites background from "Discrete-Time Geox/G/1 Retrial Queu..."

...From Aissani et al. (2014), Do (2010), Gao and Wang (2013), Gao et al. (2014), Jailaxmi et al. (2014), Li et al. (2012), Liu and Song (2013), we can find that researchers usually define four states of the server....
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Journal Article•DOI•

Strategic queueing behavior for individual and social optimization in managing discrete time working vacation queue with Bernoulli interruption schedule

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Miaomiao Yu¹, Attahiru Sule Alfa²•Institutions (2)

University of Manitoba¹, University of Pretoria²

01 Sep 2016-Computers & Operations Research

TL;DR: A discrete time working vacation queue with a utility function for the reward of receiving the service and the cost of waiting in the system and it is found that for the fully observable queue, the joining threshold for individual optimization may be less than the one for social optimization in working vacation period.

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14 citations

Journal Article•DOI•

An Unreliable Server Retrial Queue with Two Phases of Service and General Retrial Times Under Bernoulli Vacation Schedule

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Gautam Choudhury, Lotfi Tadj¹, Mitali Deka¹•Institutions (1)

Fairleigh Dickinson University¹

01 Jan 2015-Quality Technology and Quantitative Management

TL;DR: The steady state behavior of an M/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server is dealt with.

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Abstract: This paper deals with the steady state behavior of an M/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with the FCFS (first come, first served) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or serves the next unit, if any, with probability (1 – p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property. We also provide a reliabili...

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13 citations

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References

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Journal Article•DOI•

Queueing analysis: A foundation of performance evaluation: Hideaki Takagi, vol. I: Vacation and priority systems, part I (1991), xii + 488 pp., ISBN 0-444-88910-8, Vol. II: Finite systems (1993), 560 pp., ISBN 0-444-81614-3, Vol. III: Discrete-time systems (1993), 484 pp., ISBN 0-444-81611-9, North-Holland, Amsterdam

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Ho Woo Lee

01 Jan 1995-Performance Evaluation

626 citations

Journal Article•DOI•

Accessible bibliography on retrial queues

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Jesús R. Artalejo¹•Institutions (1)

Complutense University of Madrid¹

01 Aug 1999-Mathematical and Computer Modelling

397 citations

Journal Article•DOI•

A classified bibliography of research on retrial pueues: progress in 1990-1999

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Jesús R. Artalejo¹•Institutions (1)

Complutense University of Madrid¹

01 Dec 1999-Top

314 citations

"Discrete-Time Geox/G/1 Retrial Queu..." refers background in this paper

...Artalejo, J. R. and Falin, G. (2002)....
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...Further, a comprehensive comparison between retrial queues and their standard counterpart with classical waiting line can be found in Artalejo and Falin [7]....
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...For related literatures of retrial queues with vacations, the readers may refer to Artalejo [4], Krishna Kumar and Arivudainambi [20], Ke and Chang [18], Choudhury and Ke [13], and references therein for details....
[...]
...R For related literature on discrete-time retrial queues with geometric retrial times, the reader may refer to Artalejo et al. [8], Atencia and Moreno [9-10], Moreno [25], Wang and Zhao [28], Aboul-Hassan et al. [1], Liu and Gao [24] and references therein....
[...]
...For more recent references see the bibliographical overviews in Artalejo [5-6]....
[...]

Journal Article•DOI•

Accessible bibliography on retrial queues: Progress in 2000-2009

[...]

Jesús R. Artalejo¹•Institutions (1)

Complutense University of Madrid¹

01 May 2010-Mathematical and Computer Modelling

TL;DR: A bibliography on retrial queues which updates the bibliography published in this journal in Artalejo (1999) is presented, focused on the progress made during the last decade 2000-2009.

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263 citations

"Discrete-Time Geox/G/1 Retrial Queu..." refers background in this paper

...Artalejo, J. R. and Falin, G. (2002)....
[...]
...Further, a comprehensive comparison between retrial queues and their standard counterpart with classical waiting line can be found in Artalejo and Falin [7]....
[...]
...For related literatures of retrial queues with vacations, the readers may refer to Artalejo [4], Krishna Kumar and Arivudainambi [20], Ke and Chang [18], Choudhury and Ke [13], and references therein for details....
[...]
...R For related literature on discrete-time retrial queues with geometric retrial times, the reader may refer to Artalejo et al. [8], Atencia and Moreno [9-10], Moreno [25], Wang and Zhao [28], Aboul-Hassan et al. [1], Liu and Gao [24] and references therein....
[...]
...For more recent references see the bibliographical overviews in Artalejo [5-6]....
[...]

Recent Developments in Vacation Queueing Models : A Short Survey

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Jau-Chuan Ke, Chia-Huang Wu, Zhe George Zhang¹•Institutions (1)

Western Washington University¹

01 Jan 2010

TL;DR: In this paper, the authors provide a brief summary of the most recent research works on vacation queueing systems in the past 10 years, including a survey of server's vacation models.

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Abstract: Queueing systems with server vacations (server's performing non-queueing jobs) have been studied extensively since the late 70's. A considerable number of works in this area were completed in the early 80's and surveyed by Doshi in 1986. As an extension to the classical queueing system, allowing idle servers to work on non-queueing jobs makes the vacation models more applicable in a variety of systems including flexible manufacturing or service and computer communication systems. Motivated by these applications, more studies on vacation models have been done during the late 80's and 90's and surveyed in the book by Takagi in 1991 and the book by Tian and Zhang in 2006. This paper intends to provide a brief summary of the most recent research works on vacation queueing systems in the past 10 years. Keywords  server's vacation, batch arrivals, modified vacation policy, working vacations, multi-server vacation models.

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136 citations