Title: On the distribution of an infinite-buffer queueing system with versatile bulk-service rule under batch-size-dependent service policy: M/Gn(a,Y) /1

Authors: Sourav Pradhan

Addresses: Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur-440010, India

Abstract: Batch-service queues have a wide range of noteworthy applications in wireless telecommunication to deal with the multimedia type of data, manufacturing systems, group testing procedure, etc. The knowledge of both the queue and server content distributions helps the system designer to evaluate the efficiency of the queueing system in a better way. We analyse a single server infinite-buffer batch-size-dependent service queue with Poisson arrival and versatile batch-service rule. Based on supplementary variable technique, a bivariate probability generating function, the entire spectrum of new contributions, of queue content and number in a served batch at departure epoch is derived. Moreover, we perceive the complete queue and server content distribution at departure as well as arbitrary epochs. The utility of analytical results is illustrated by the inclusion of some numerical examples, which also includes the investigation of multiple zeroes.

Keywords: batch-service; versatile-bulk-service; batch-size-dependent; multiple roots; queueing; server content.

DOI: 10.1504/IJMOR.2020.106908

International Journal of Mathematics in Operational Research, 2020 Vol.16 No.3, pp.407 - 434

Received: 22 Oct 2018
Accepted: 01 Feb 2019

Published online: 22 Apr 2020 *

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