Stationary queue and server content distribution of a batch-size-dependent service queue with batch Markovian arrival process: BMAP/Gn(a,b)/1

Pradhan, Sourav; Gupta, Umesh C.

doi:10.1080/03610926.2020.1813304

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…Neuts [ 22 ] proposed the GBS rule which is the most popular batch service rule in queueing literature in which the customers get serves in packets with lower threshold a and upper threshold b . For the specific analysis of batch service queue, we mention Chaudhry and Templeton [ 5 ] and Medhi [ 21 ], and for the current status on the literature of batch service queue, readers are invoked to see [ 1 – 3 , 10 , 24 ] and the references therein. In the batch service queue, the idle period of the server may be utilized in a customized manner by entangling the server in some secondary job.…”

Section: Introductionmentioning

confidence: 99%

Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation

Tamrakar

Banerjee

2021

Int. J. Appl. Comput. Math

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Section: Introductionmentioning

confidence: 99%

Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation

Tamrakar

Banerjee

2021

Int. J. Appl. Comput. Math

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“…Our main objective of acquiring the bivariate pgf can be accomplished by substituting θ = λ−λz in (32). Division of the resulting expression by…”

Section: Model Descriptionmentioning

confidence: 99%

“…The application further stretches to the wireless telecommunication systems, recreational devices in amusement parks, chemical processing industries, etc. Recent developments and more applications can be found in Claeys et al [10,11,13], Banerjee et al [4,6,16], Pradhan and Gupta [31,32,33].…”

mentioning

confidence: 99%

Performance analysis of an infinite-buffer batch-size-dependent bulk service queue with server breakdown and multiple vacation

Pradhan

Karan

2023

JIMO

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<p style='text-indent:20px;'>In several manufacturing systems, server's breakdown is a common phenomenon for which renovation of the service station is required and has a definite effect on the system. The server's vacation is a significant tool to deal with the systems where a common server is shared by several users. The principal goal of this paper is to analyze a batch-service queueing model with server's breakdown, multiple vacations and batch-size-dependent service time. To be more precise, the center of attention is on the queue length together with server content distribution for which we obtain the bivariate probability generating function using supplementary variable technique. Server content distribution is very worthy for the manufacturing systems. The probabilities have been extracted and used to acquire the arbitrary epoch probabilities. In order to upgrade the qualitative aspects of the concerned model, diverse numerical results and graphical observations are illustrated.</p>

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“…In this paper we are assuming that all the roots of Υ(x) = 0 are distinct, for repeated roots slight modification is needed. For that, one may refer to Pradhan and Gupta [22,23].…”

Section: Extraction Of Probability Vectors From Bivariate Vgfmentioning

confidence: 99%

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1

et al. 2021

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Discrete-time queueing models find a large number of applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems and computer networks. In this paper, we analyze an infinite-buffer queueing model with discrete Markovian arrival process. The units on arrival are served in batches by a single server according to the general bulk-service rule, and the service time follows general distribution with service rate depending on the size of the batch being served. We mathematically formulate the model using the supplementary variable technique and obtain the vector generating function at the departure epoch. The generating function is in turn used to extract the joint distribution of queue and server content in terms of the roots of the characteristic equation. Further, we develop the relationship between the distribution at the departure epoch and the distribution at arbitrary, pre-arrival and outside observer's epochs, where the first is used to obtain the latter ones. We evaluate some essential performance measures of the system and also discuss the computing process extensively which is demonstrated by some numerical examples.

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Stationary queue and server content distribution of a batch-size-dependent service queue with batch Markovian arrival process: BMAP/Gn(a,b)/1

Cited by 6 publications

References 27 publications

Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation

Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation

Performance analysis of an infinite-buffer batch-size-dependent bulk service queue with server breakdown and multiple vacation

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1

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Stationary queue and server content distribution of a batch-size-dependent service queue with batch Markovian arrival process: BMAP/Gn(a,b)/1

Cited by 6 publications

References 27 publications

Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation

Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation

Performance analysis of an infinite-buffer batch-size-dependent bulk service queue with server breakdown and multiple vacation

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/Gn(a,b)/1

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Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1