Title: Transient analysis of an M/M/1 queue with a repairable server and multiple vacations

Authors: K. Kalidass; J. Gnanaraj; S. Gopinath; Ramanath Kasturi

Addresses: Department of Mathematics, P.S.R. Engineering College, Sivakasi-626 140, India ' Department of Mathematics, Alagappa University Arts and Science College, Paramakudi-623 707, Tamil Nadu, India ' Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar-626 001, Tamil Nadu, India ' School of Mathematics, Madurai Kamaraj University, Madurai-625 021, India

Abstract: In this paper, we discuss the time dependent behaviour of an M/M/1 queueing system with multiple vacations. We assume that the system is subject to sudden breakdowns and that during this period the system is flushed out. After the repair, the server waits for the arrival of the next customer. We have obtained analytical expressions for the transient state probabilities of the system size. We also obtain expressions for the transient expected value and variance of the system length. The corresponding steady state results are derived. We have performed a busy period analysis of this system in the steady state. We have obtained analytical expressions for the expected duration of a busy period and the expected duration of the vacation period. We present numerical examples to illustrate the sensitivity of the performance measures of the system to the changes in the parameters of the system.

Keywords: Markovian queues; time dependent analysis; multiple vacations; repairable servers; busy period analysis; transient analysis.

DOI: 10.1504/IJMOR.2014.059522

International Journal of Mathematics in Operational Research, 2014 Vol.6 No.2, pp.193 - 216

Received: 10 Jan 2012
Accepted: 27 Sep 2012
Published online: 28 Jun 2014 *

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