Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots

Samanta, S. K.; Chaudhry, M. L.; Pacheco, Antònio; Gupta, Umesh C.

doi:10.1016/j.cor.2014.10.017

Cited by 12 publications

(5 citation statements)

References 14 publications

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“…It may be noted here that Chaudhry et al (2012) obtained analytically explicit expressions for steadystate probabilities for GI/C-MSP/1 queue using roots. Further, Samanta et al (2015) have carried out the discrete-time analysis of GI/D-MSP/1/∞ model using roots. Although this paper is an extension of Chaudhry et al (2012) to the batch arrival of variable capacity, we have carried out waiting-time analysis as well, one root approximation, derivation of expected busy and idle periods and extensive numerical results.…”

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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“…It is hoped that numerical results presented in this paper may assist to both theoreticians and practitioners who would like to tally their results against ours when they use other methods. We have checked our results for single arrival GI/D-M SP/1/∞ queue given by Samanta et al [33] and found that the results matched perfectly. Tables 2 and 8, the mean queue-length (L q ) and the mean waiting-time in the queue (W q ) of an arbitrary customer in an arrival batch using Little's rule.…”

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confidence: 53%

“…Samanta and Zhang [35] carried out the analysis of the discrete-time GI/D-M SP/1 queue with multiple vacations using the matrix-geometric method wherein the new service process starts with the initial phase distribution independent of the path followed by the previous service process when the server returns from a vacation and finds at least one waiting customer. Samanta et al [33] analyzed discrete-time GI/D-M SP/1 queueing system using the method roots under the late arrival system with delayed access (LAS-DA) assuming that the service process is interrupted during idle periods of the system. Wang et al [37] analyzed the packet loss pattern of the finite-buffer D-BM AP/D-M SP/1 queueing system using the matrix-geometric approach.…”

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confidence: 99%

“…where P(0, 0) = I m and P(n, k) = 0, n > k ≥ 0. As the service phase does not change during idle periods of the system, let P(n, k), n ≥ 1, k ≥ 0, be the square matrices of order m defined in Samanta et al [33] represent that n customers are served in k time slots. Therefore, the matrices P(n, k), n ≥ 1, k ≥ 0, satisfy…”

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confidence: 99%

“…Appendix A. . One may remark here that Samanta et al [33] analyzed the GI/D-M SP/1/∞ queue with the LAS-DA case only. Due to the discussion of LAS-DA, they obtained the simplified forms of Ω n , n ≥ 0, S n , n ≥ 2, D 1 , Υ 0 , χ n , n ≥ 2, and Γ 1 .…”

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confidence: 99%

See 2 more Smart Citations

Analysis of $GI^{[X]}/D$-$MSP/1/\infty$ queue using $RG$-factorization

Samanta¹,

Nandi²

2021

Journal of Industrial &Amp; Management Optimization

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This paper analyzes an infinite-buffer single-server queueing system wherein customers arrive in batches of random size according to a discretetime renewal process. The customers are served one at a time under discretetime Markovian service process. Based on the censoring technique, the UL-type RG-factorization for the Toeplitz type block-structured Markov chain is used to obtain the prearrival epoch probabilities. The random epoch probabilities are obtained with the help of classical principle based on Markov renewal theory. The system-length distributions at outside observer's, intermediate and post-departure epochs are obtained by making relations among various time epochs. The analysis of waiting-time distribution measured in slots of an arbitrary customer in an arrival batch has also been investigated. In order to unify the results of both discrete-time and its continuous-time counterpart, we give a brief demonstration to get the continuous-time results from those of the discrete-time ones. A variety of numerical results are provided to illustrate the effect of model parameters on the performance measures.

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Two approximations of renewal function for any arbitrary lifetime distribution

Jiang

2019

Ann Oper Res

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Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots

Cited by 12 publications

References 14 publications

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 / ∞

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 / ∞

Analysis of $GI^{[X]}/D$-$MSP/1/\infty$ queue using $RG$-factorization

Two approximations of renewal function for any arbitrary lifetime distribution

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