Poisson queues with Markov modulated service rates

R. Sivasamy, N. Paranjothi, Keoagile Thaga and G. Paulraj

International Journal of Mathematics in Operational Research, 2021, vol. 19, issue 2, 145-160

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. (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.inderscience.com/link.php?id=116317 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ids:ijmore:v:19:y:2021:i:2:p:145-160

Access Statistics for this article

More articles in International Journal of Mathematics in Operational Research from Inderscience Enterprises Ltd
Bibliographic data for series maintained by Sarah Parker ().