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Entropy 2019, 21(3), 259; https://doi.org/10.3390/e21030259

Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns

1
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2
Department of Industrial Engineering, Alfaisal University, Riyadh 12714, Saudi Arabia
3
Department of Computer Engineering, King Saud University, Riyadh 11453, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 6 February 2019 / Revised: 26 February 2019 / Accepted: 1 March 2019 / Published: 7 March 2019
(This article belongs to the Special Issue Information Theory and Stochastics for Multiscale Nonlinear Systems)
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Abstract

A flexible single-server queueing system is considered in this paper. The server adapts to the system size by using a strategy where the service provided can be either single or bulk depending on some threshold level c. If the number of customers in the system is less than c, then the server provides service to one customer at a time. If the number of customers in the system is greater than or equal to c, then the server provides service to a group of c customers. The service times are exponential and the service rates of single and bulk service are different. While providing service to either a single or a group of customers, the server may break down and goes through a repair phase. The breakdowns follow a Poisson distribution and the breakdown rates during single and bulk service are different. Also, repair times are exponential and repair rates during single and bulk service are different. The probability generating function and linear operator approaches are used to derive the system size steady-state probabilities. View Full-Text
Keywords: Markovian queue; flexible server; unreliable server; steady-state distribution; linear operator Markovian queue; flexible server; unreliable server; steady-state distribution; linear operator
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Bounkhel, M.; Tadj, L.; Hedjar, R. Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns. Entropy 2019, 21, 259.

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