Reliability analysis of M/G/1 queueing system with repairable service station of reliability series structure

Cao, Jiling

doi:10.1016/0026-2714(94)90035-3

Cited by 25 publications

(26 citation statements)

References 13 publications

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“…This results in a period of unavailable time until the servers are repaired. Such a system with repairable server has been studied as a queueing model and reliability model by many authors, see [8][9][10] In this paper, we study the same system in [7] with the further assumption that the server may be subject to breakdowns and repairs in the two service processes. The present study was motivated by the fast-expanding area of tele-services, which prominently include telephone call centers and the emerging internet-based market (see [11]).…”

Section: Introductionmentioning

confidence: 99%

An M/G/1 queue with second optional service and server breakdowns

Wang

2004

Computers & Mathematics with Applications

104

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AnM/G/1 with second optional service and unreliable server is studied in this paper.We assume that customers arrive to the system according to a Poisson process with rate A. All demand the first "essential" service, whereas only some of them demand the second "optional" service. The service times of the first essential service are i.i.d, random variables, and that of the second optional service are i.i.d, exponential random variables. We assume that the server has a servicephase dependent, exponentially distributed life time as well as a service-phase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.

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Section: Introductionmentioning

confidence: 99%

An M/G/1 queue with second optional service and server breakdowns

Wang

2004

Computers & Mathematics with Applications

104

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“…Clearly, χ n includes the down time of the server due to server failures during the service period of the nth customer. It is easy to see, for example from Cao and Chen (1982), that the sequenceχ n for n ≥ 1 are i.i.d. random variables and E[χ n ] = 1 μ (1 + α β ).…”

Section: The System Of Differential Equationsmentioning

confidence: 98%

“…(ii) For the generalized service time, it has been illustrated that the life time of the server is a most crucial factor. When the life time of the server is exponential, the distribution of the generalized service time was given in Cao and Chen (1982) and Gnedenko and Kovalenko (1989). When the life time of the server is non-exponential and phase type, the distribution of the generalized service time was provided in Li (1996) for an M/SM(P H/SM)/1 repairable queue and Li, Tan and Sun (1999) for a SM/P H(P H/P H)/1 repairable queue.…”

Section: Introductionmentioning

confidence: 99%

“…Since the reliability indices are irrelevant to the computations of the queueing indices, the generalized service time is not helpful for computing the reliability indices. The stationary availability and the stationary failure frequency were given in Cao and Chen (1982), Li (1996), Li, Shi and Chao (1997), Li, Tan and Sun (1999) and Wang, Cao and Li (2001). (iv) For a blockstructured repairable queue, , Li (1996), Li, Tan and Sun (1999) and Li and Cao (2000) applied the matrix-analytic method to derive the stationary availability and failure frequency.…”

Section: Introductionmentioning

confidence: 99%

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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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“…It is easy to see that χ (0) n is independent of n (n = 1, 2, · · ·). According to our model, repeated calls have no effects on χ (0) n , so some results obtained by Cao and Cheng [11] can be used here. It has been shown that the generalized successive service…”

Section: The Steady-state Equationsmentioning

confidence: 99%

A single server retrial queue with general retrial times and two-phase service

Wang

Li²

2009

J Syst Sci Complex

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An M/G/1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline. All customers demand the first "essential" service, whereas only some of them demand the second "optional" service, and the second service is multioptional. During the service, the server is subject to breakdown and repair. Assume that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures of interest.

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Reliability analysis of M/G/1 queueing system with repairable service station of reliability series structure

Cited by 25 publications

References 13 publications

An M/G/1 queue with second optional service and server breakdowns

An M/G/1 queue with second optional service and server breakdowns

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

A single server retrial queue with general retrial times and two-phase service

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