A<i>G/SM/1</i>queue with vacations depending on service times

Machihara, Fumiaki

doi:10.1080/15326349508807366

Cited by 10 publications

(10 citation statements)

References 22 publications

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“…More generalized service process, namely semi-Markov process was discussed by several researchers. For example, G/SM/1/∞ queueing system with vacations was considered by Machihara (1995). It may be remarked here that Gupta and Banik (2007) have carried out the analysis of finite-as well as infinite-buffer GI/C-MSP/1 queue.…”

Section: Introductionmentioning

confidence: 99%

A simple analysis of the batch arrival queue with infinite-buffer and Markovian service process using roots method: $$ GI ^{[X]}/C$$ G I [ X ] / C - $$ MSP /1/\infty $$ M S P / 1 / ∞

2015

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We consider a batch arrival infinite-buffer single-server queue with generally distributed inter-batch arrival times with arrivals occurring in batches of random sizes. The service process is correlated and its structure is governed by a Markovian service process in continuous time. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution at a pre-arrival epoch. We also obtain the steady-state probability distribution at an arbitrary epoch using the classical argument based on Markov renewal theory. Some important performance measures such as the average number of customers in the system and the mean sojourn time have also been obtained. Later, we have established heavy-and light-traffic approximations as well as an approximation for the tail probabilities at pre-arrival epoch based on one root of the characteristic equation. Numerical results for some cases have been presented to show the effect of model parameters on the performance measures.

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Section: Introductionmentioning

confidence: 99%

A simple analysis of the batch arrival queue with infinite-buffer and Markovian service process using roots method: $$ GI ^{[X]}/C$$ G I [ X ] / C - $$ MSP /1/\infty $$ M S P / 1 / ∞

2015

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“…Machihara [19] generalized the system in [18] to the case with the removable server and semi-Markovian control of vacations.…”

Section: Introductionmentioning

confidence: 99%

“…The second way to generalize the chains in [18,19] consists of increasing the dimensionality of the quasitoeplitz Markov chain. We consider an M-dimensional quasitoeplitz Markov chain, which has one of denumerable and M-1 finite components.…”

Section: Introductionmentioning

confidence: 99%

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Multi‐dimensional quasitoeplitz Markov chains

Dudin

Klimenok

1998

International Journal of Stochastic Analysis

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“…Alfa et al (2000) discussed the asymptotic behaviour of the GI/MSP/1 queue using perturbation theory. The G/SM/1/∞ queueing system with vacations was considered by Machihara (1995). However, to the best of authors' knowledge there are no studies available on MSP with renewal input of batches of random size.…”

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confidence: 99%