Title: Exact stationary solution for a fluid queue driven by an M/M/1 queue with disaster and subsequent repair

Authors: K.V. Vijayashree; A. Anjuka

Addresses: Department of Mathematics, Anna University, Chennai, India ' Department of Mathematics, SRM Institute of Science and Technology, Kancheepuram, India

Abstract: This paper deals with the stationary analysis of a fluid queuing model driven by an M/M/1 queue subject to disaster and subsequent repair. Further, arrivals are allowed to join the background queuing model during the period of repair at a slower rate as compared to the arrivals during regular busy period of the server. Such a model was analysed earlier by Ammar (2014), however the model formulation and hence the main results are found to be incorrect. In this paper, the assumptions are suitably modified to ensure correctness, detailed mathematical analysis is carried out to find an explicit analytical expression for the buffer content distribution. The underlying system of differential difference equations that govern the process are solved using Laplace transform and generating function methodologies. The closed form expressions for the joint steady state probabilities of the state of the background queuing model and the content of the buffer are obtained in terms of modified Bessel function of the first kind.

Keywords: generating function; Laplace transform; steady state probabilities; buffer content distribution.

DOI: 10.1504/IJMOR.2019.101614

International Journal of Mathematics in Operational Research, 2019 Vol.15 No.1, pp.92 - 109

Received: 24 Feb 2017
Accepted: 28 Jan 2018
Published online: 14 Aug 2019 *

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