Queue Length and Server Content Distribution in an Infinite-Buffer Batch-Service Queue with Batch-Size-Dependent Service

Gupta, Umesh C.; Pradhan, Sourav

doi:10.1155/2015/102824

Cited by 10 publications

(4 citation statements)

References 8 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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“…Pradhan et al (2016a) analyzed an infinite-buffer batch-arrival and batch service queue under batchsize-dependent service policy. Gupta and Pradhan (2015) discussed the queue length and server content distribution in an infinite buffer batch service queue with batch size dependent service. They studied M=G a;b ð Þ n =1 queue and derived a bivariate probability generating function (PGF) of both queue content and number with the departing batch.…”

Section: Literature Reviewmentioning

confidence: 99%

Modelling and simulation analysis of a bulk queueing system

Nithya

Haridass

2019

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Purpose The purpose of this paper is to provide simulation modelling for bulk arrival bulk service queueing system involved in a textile industry and analyze the performance metrics. Design/methodology/approach This paper describes the simulation modelling of a bulk queueing system with limited number of admissions and multiple vacations. The model is developed for the proposed queueing system using Flexsim 2017, and it is explained through an application observed in a textile industry involving the process of cone winding. Findings In this paper, the simulation model has been developed to study the behaviour of queues at different resources in a production system. Various performance measures such as average components, average waiting time, total number of inputs and outputs, processing time and idle time involved in a textile industry are evaluated using simulation and justified through numerical illustration. Practical implications The proposed simulation model may be used in various scenarios wherever a real time situation exists related to bulk queueing system. The results produced in this paper can be used by the manufacturing industries to enhance the need-based accuracy. It is worth pointing out that the findings are of direct practical relevance and can be successfully used for a number of industrial applications. Originality/value The approach suggested in this paper attempts to deal with the queueing system involved in a textile industry and provides numerical results in less time with less computer resources. It provides a reasonably good approximation for simple and complex queueing models where it is difficult to find closed form of theoretical results.

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“…For these purposes, the queue length and server content distribution together gives an inner feeling about the queueing model. In view of this, Gupta and Pradhan (2015), Gupta (2016, 2017)…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution of an infinite-buffer batch-arrival and batch-service queue with random serving capacity and batch-size-dependent service

Pradhan

Gupta

2021

IJOR

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In traditional batch-service queueing systems, the mean service time of batches are generally assumed to be constant. However, in numerous applications this assumption may not be appropriate. In telecommunication networks, the transmission rates depend on the number of packets in the batch which can be framed as batch-size-dependent service queue. The objective of this paper is to focus on both queue and server content distribution in an infinite-buffer batch-arrival and batch-service queue with random serving capacity rule and batch-size-dependent service. After deriving a bivariate probability generating function of queue length and server content distribution at departure epoch of a batch, we extract the complete joint distribution in terms of roots of the characteristic equation. We also obtain the system as well as queue length distribution at arbitrary epoch. Finally, a significant number of numerical examples are appended to show the feasibility of the analytic procedure and results where the occurrence of multiple roots have been dealt without facing any difficulty. At the end, a graphical representation of cost of the system shows that batch-size-dependent service is more significant as compared to batch-size-independent service.

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Queue Length and Server Content Distribution in an Infinite-Buffer Batch-Service Queue with Batch-Size-Dependent Service

Cited by 10 publications

References 8 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

Modelling and simulation analysis of a bulk queueing system

Stationary distribution of an infinite-buffer batch-arrival and batch-service queue with random serving capacity and batch-size-dependent service

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