Article: Stationary distribution of an infinite-buffer batch-arrival and batch-service queue with random serving capacity and batch-size-dependent service Journal: International Journal of Operational Research (IJOR) 2021 Vol.40 No.1 pp.1 - 31 Abstract: 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. Inderscience Publishers - linking academia, business and industry through research

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

Authors: S. Pradhan; U.C. Gupta

Addresses: Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur – 831014, India ' Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur – 721302, India

Abstract: 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.

Keywords: batch-arrival; batch-size-dependent; random serving capacity; supplementary variable; queueing; joint distribution.

DOI: 10.1504/IJOR.2021.111951

International Journal of Operational Research, 2021 Vol.40 No.1, pp.1 - 31

Received: 18 Sep 2017
Accepted: 25 Mar 2018
Published online: 22 Dec 2020 *

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Title: 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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