• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.343-350
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• 2015

We consider an M^X/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the M^X/G/1 retrial queue.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.3
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• pp.247-255
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• 2002

The objective of this paper is to clarify the decomposition property for $M^{X}$/G/1 queues with generalized vacations so that the decomposition property is better understood and becomes more applicable. As an example model, we use the $M^{X}$/G/1 queue with setup time. For this queue, we correct Choudhry's (2000) steady-state queue size PGF and derive the steady-state waiting time LST. We also present a meaningful interpretation for the decomposed steady-state waiting time LST.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.2
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• pp.51-61
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• 2002

By using the arrival time approach of Chae et at. [6], we derive various performance measures including the queue length distributions (in PGFs) and the waiting time distributions (in LST and PGF) for both M$^{x}$ /G/1 and Geo$^{x}$ /G/1 queueing systems, both under the assumption that the server, when it becomes idle, takes multiple vacations up to a random maximum number. This is an extension of both Choudhury[7] and Zhang and Tian [11]. A few mistakes in Zhang and Tian are corrected and meaningful interpretations are supplemented.

• Management Science and Financial Engineering
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• v.12 no.2
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• pp.1-18
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• 2006

We consider an $M^x/G/1$ queueing system with Bernoulli vacation schedule under multiple vacation policy. where after each vacation completion or service completion the server takes sequence of vacations until a batch of new customer arrive. This generalizes both $M^x/G/1$ queueing system with multiple vacation as well as M/G/1 Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further attempts have been made to unify the results of related batch arrival vacation models.

• Management Science and Financial Engineering
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• v.15 no.2
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• pp.1-21
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• 2009

We consider an $M^x/G/1$ queueing system with a random setup time under Bernoulli vacation schedule, where the service of the first unit at the completion of each busy period or a vacation period is preceded by a random setup time, on completion of which service starts. However, after each service completion, the server may take a vacation with probability p or remain in the system to provide next service, if any, with probability (1-p). This generalizes both the $M^x/G/1$ queueing system with a random setup time as well as the Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further, attempts have been made to unify the results of related batch arrival vacation models.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.419-438
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• 1995

We investigate a tansient diffusion approximation of queue size distribution in $M^{X}/G^{Y}/c$ system using the diffusion process with elementary return boundary. We choose an appropriate diffusion process which approxiamtes the queue size in the system and derive the transient solution of Kolmogorov forward equation of the diffusion process. We derive an approximation formula for the transient queue size distribution and mean queue size, and then obtain the stationary solution from the transient solution. Accuracy evalution is presented by comparing approximation results for the mean queue size with the exact results or simulation results numerically.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.04a
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• pp.229-229
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• 1993

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.425-433
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• 2017

This paper is concerned with the analysis of the busy period distribution in a batch arrival $M^X/G/1$ retrial queue. The expression for the Laplace-Stieltjes transform of the length of the busy period is well known, but from this expression we cannot compute the moments of the length of the busy period by direct differentiation. This paper provides a direct method of calculation for the first and second moments of the length of the busy period.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.36-48
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• 1991

In this study, an efficient algorithm is developed to compute steady state probabilities for the following M$_{x}$G/1 server vacation system under control-operating poligy: At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length at this time is equal to or greater than a prespecified threshold value r, he begins to serve the queue until it is empty.y.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.491-507
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• 2002

We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.