Performance analysis of a single server retrial queue with working vacation

Arivudainambi, D.; Godhandaraman, P.; Rajadurai, P.

doi:10.1007/s12597-013-0154-1

Cited by 41 publications

(13 citation statements)

References 17 publications

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“…Using the matrix-analytic method, Tao et al [16] considered an M/M/1 retrial queue with collisions and working vacation interruption under N-policy, Upadhyaya [26] analyzed a discrete-time Geo X /Geo/1 retrial queue with working vacations. Using the method of supplementary variable, Aissani et al [1] and Jailaxmi et al [28] both generalized the model of [27] to an M/G/1 queue with constant retrial policy, and Arivudainambi et al [4] analyzed an M/G/1 queue with general retrial time policy. Gao et al [24] discussed an M/G/1 retrial queue with general retrial times and working vacation interruption, the discrete-time Geo X /G/1 queue was investigated by Gao and Wang [23].…”

Section: Introductionmentioning

confidence: 99%

An M/G/1 retrial queue with single working vacation under Bernoulli schedule

Zhang

Gao

2020

RAIRO-Oper. Res.

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In this paper, an M/G/1 retrial queue with general retrial times and single working vacation is considered. We assume that the customers who find the server busy are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline and only the customer at the head of the queue is allowed access to the server. During the normal period, if the orbit queue is not empty at a service completion instant, the server begins a working vacation with specified probability q (0 ≤ q ≤ 1), and with probability 1 − q, he waits for serving the next customer. During the working vacation period, customers can be served at a lower service rate. We first present the necessary and sufficient condition for the system to be stable. Using the supplementary variable method, we deal with the generating functions of the server state and the number of customers in the orbit. Various interesting performance measures are also derived. Finally, some numerical examples and cost optimization analysis are presented.Mathematics Subject Classification. 60k25, 90B22.

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Section: Introductionmentioning

confidence: 99%

An M/G/1 retrial queue with single working vacation under Bernoulli schedule

Zhang

Gao

2020

RAIRO-Oper. Res.

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“…Retrial queueing system plays a major role in communication systems and networks. Recently, some of the authors like Arivudainambi et al [1], Artalejo and Gomez-Corral [2], Choudhury and Deka [3], Rajadurai et al [5,6], Servi and Finn [7] have developed a queueing models with different aspects. In this paper, "we have extended the concepts of multi phase of service, optional re-service, multiple working vacations, vacation interruption, breakdowns and repair from the work of Arivudainambi et al [1]".…”

Section: Introductionmentioning

confidence: 99%

“…first and second moments are (1) (2) and ii  for (i=1,2,…,k). From this model, the modified service time or the time required by the customer to complete the service cycle is a random variable S is given…”

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confidence: 99%

An M/G/1 Retrial Queueing System with Phase Type Services and Working Vacations

Rajadurai¹,

Santhoshi²,

Pavithra³

et al. 2018

IJET

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“…Choudhury and Deka [10] discussed a single server retrial queueing system with two phases of service subject to server breakdown and Bernoulli vacation. Arivudainambi et al [2] discussed a retrial queueing system with single working vacation. Further, Choudhury and Ke [11] have developed queueing models with the concept of general retrial times along with Bernoulli vacation schedule.…”

Section: Introductionmentioning

confidence: 99%

“…Let X k denote the number of customers belonging to the k th arrival batch, where X k , k=1, 2, 3…are identically and independently distributed (i.i.d) random variables (r.v) with a common distribution Pr[X k =n]=χ n , n=1,2,3… and X(z) denotes the probability generating function (PGF) of X. We denote E(X)=X [1] and E(X(X-1))=X [2] as the first and second factorial moments of r.v. X.…”

Section: Introductionmentioning

confidence: 99%

Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule

2015

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In this paper, we consider a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers. Any arriving batch of positive customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. Arriving positive customers may balk (or renege) the system at particular times. After completion of service the unsatisfied positive customer may rejoin into the orbit to get another regular service as feedback customer. The server takes Bernoulli vacation after service completion of positive customers. After completion of service (if the server is not taking vacation), repair or vacation the server searches for the customers in the orbit or remains idle. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some system performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.

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Performance analysis of a single server retrial queue with working vacation

Cited by 41 publications

References 17 publications

An M/G/1 retrial queue with single working vacation under Bernoulli schedule

An M/G/1 retrial queue with single working vacation under Bernoulli schedule

An M/G/1 Retrial Queueing System with Phase Type Services and Working Vacations

Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule

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