A retrial queue with redundancy and unreliable server

Aïssani, Amar

doi:10.1007/bf01158703

Cited by 49 publications

(23 citation statements)

References 21 publications

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“…Retrial queues with unreliable servers have been discussed by some researchers, among whom are Kulkarni and Choi (1990), Yang and Li (1994), Artalejo (1994), Aissani (1994), Aissani and Artalejo (1998), Artalejo and Gómez-Corral (1998) and Wang, Cao and Li (2001). In this paper, a BMAP/G/1 retrial queue with server breakdowns and repairers is considered both from the queueing viewpoint and from the reliability viewpoint, which is a more general class of retrial queues than those in literature.…”

Section: Introductionmentioning

confidence: 97%

A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs

Zhao

2006

Ann Oper Res

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In this paper, we consider a BMAP/G/1 retrial queue with a server subject to breakdowns and repairs, where the life time of the server is exponential and the repair time is general. We use the supplementary variable method, which combines with the matrix-analytic method and the censoring technique, to study the system. We apply the RG-factorization of a level-dependent continuous-time Markov chain of M/G/1 type to provide the stationary performance measures of the system, for example, the stationary availability, failure frequency and queue length. Furthermore, we use the RG-factorization of a level-dependent Markov renewal process of M/G/1 type to express the Laplace transform of the distribution of a first passage time such as the reliability function and the busy period. KeywordsRetrial queues . Batch Markov arrival processes (BMAP) . Markov chains of M/G/1 type . Markov renewal processes of M/G/1 type . Supplementary variable method . Matrix-analytic method . Censoring technique . RG-factorization . Reliability

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Section: Introductionmentioning

confidence: 97%

A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs

Zhao

2006

Ann Oper Res

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“…Wang et al [10] carried out a detailed analysis of reliability of the classic M/G/1 retrial queues with exponentially distributed retrial times. For related literature, interested readers may refer to [11][12][13][14], and references therein.…”

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confidence: 99%

On the single server retrial queue with priority subscribers and server breakdowns

Wang

2008

J Syst Sci Complex

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The author concerned the reliability evaluation as well as queueing analysis of M 1 , M 2 /G 1 , G 2 /1 retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case of blocking, the first type of customers can be queued whereas the second type of customers must leave the service area but return after some random period of time to try their luck again. The author assumes that the server is unreliable and it has a service-type dependent, exponentially distributed life time as well as a service-type dependent, generally distributed repair time. The necessary and sufficient condition for the system to be stable is investigated. Using a supplementary variable method, the author obtains a steady-state solution for queueing measures, and the transient as well as the steady-state solutions for reliability measures of interest.

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“…Then {S (k) } are independently and identically distributed with Laplace transform B*(s)=B 1 *(s+ 1 …”

Section: Proofmentioning

confidence: 99%

“…Wang [17], Wang and Li [18], Atencia et. al [6], Geni Gupur [11] and Aissani [1] have studied retrial queueing system with random breakdown. In most of the articles with server breakdown it is assumed that the failed service channel undergoes repair instantaneously.…”

Section: Introductionmentioning

confidence: 99%

Bulk Arrival Two Phase Retrial Queueing System with Impatient Customers, Orbital Search, Active Breakdowns and Delayed Repair

Bagyam¹,

Chandrika²,

Rani³

2013

IJCA

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Bulk arrival general service retrial queueing system is analyzed in this paper. Server provides two phases of serviceessential and optimal. After each service completion, the server searches for customers in the orbit. Customers may balk or renege at particular times. Accidental and active breakdown of the server is considered. The repair of the failed server starts after a random amount of time known as delay time. After repair the server continues the service of the interrupted customer or waits for the same customer. The necessary and sufficient condition for the system to be stable is presented. By applying supplementary variable technique, the steady state distributions of the server state and the number of customers in the orbit are obtained. Numerical examples are presented to illustrate the influence of the parameters on several performance characteristics

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A retrial queue with redundancy and unreliable server

Cited by 49 publications

References 21 publications

A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs

A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs

On the single server retrial queue with priority subscribers and server breakdowns

Bulk Arrival Two Phase Retrial Queueing System with Impatient Customers, Orbital Search, Active Breakdowns and Delayed Repair

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