Title: A single server finite buffer Geom/ G/1/ K queue with L limited service and multiple vacation policy

Authors: K. Sikdar

Addresses: Department of Mathematics, BMS Institute of Technology and Management, Post Box No. 6443, Doddaballapura Main Road, Yelahanka, Bangalore-560064, India; Affiliated to: Visvesvaraya Technological University (VTU), India

Abstract: This paper investigates a Geom/ G/1/ K queueing system with L limited service and multiple vacation in which the packets arrive under the Bernoulli process. The lengths of service and vacation times are integral multiples of the slot duration. The server goes for a vacation if either the system is empty or L packets have been served during each busy period. The queue length distribution at service completion and vacation termination epochs is obtained using the imbedded Markov chain technique. Based on the supplementary variable technique, we develop the system of difference equations to derive the queue length distribution at random epoch. The waiting-time analysis for an arrival packet and other performance measures are also examined. We execute several numerical results, but only a few of them are added in the form of tables and graphs. The results of this research could be useful in understanding the performance of a service system.

Keywords: discrete-time queue; finite-buffer; limited service discipline; imbedded Markov chain; multiple vacation policy.

DOI: 10.1504/IJMOR.2024.138058

International Journal of Mathematics in Operational Research, 2024 Vol.27 No.3, pp.328 - 353

Received: 16 Sep 2021
Accepted: 03 Jun 2022
Published online: 18 Apr 2024 *

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