Title: Poisson queues with Markov modulated service rates

Authors: R. Sivasamy; N. Paranjothi; Keoagile Thaga; G. Paulraj

Addresses: Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana, South Africa ' Department of Statistics, Annamalai University, Annamalainagar, Tamil Nadu, India ' Department of Statistics, University of Botswana, Gaborone, Botswana, South Africa ' Department of Statistics, Annamalai University, Annamalainagar, Tamil Nadu, India

Abstract: In this paper we investigate an M/MM/1 queueing system that makes transitions between two service rates 'S(slow) and F(fast)' only at service completion epochs. Switching between these 'S and F' states occurs according to an embedded Markov chain rule. Both inter arrival times and service times follow exponential distributions. We also discuss an extension for an M/MM/1/(0, N] ∪ (N, ∞) system. Under steady state conditions, the stationary probability distribution for the system size is obtained by spectral expansion method. To exemplify the tractability of the dynamics of the switching probabilities on the offered work load and the mean waiting time, we provide numerical illustrations.

Keywords: Markov modulated service; fast and slow service rates; stationary probability distribution.

DOI: 10.1504/IJMOR.2021.116317

International Journal of Mathematics in Operational Research, 2021 Vol.19 No.2, pp.145 - 160

Received: 12 Sep 2019
Accepted: 20 Feb 2020
Published online: 20 Jul 2021 *

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