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© 2023. This work is published under https://creativecommons.org/licenses/by-nc-nd/4.0/ (the“License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

An M/M/3 repairable Markovian queueing system with servers on vacation has been taken into consideration. The service rates of the servers in this system differ. Each server is allowed to go on its own vacation when there are no customers in system. At the end of the vacation period, if the system is empty, then servers take another vacation; otherwise, they turn on to the busy state. Besides, a breakdown may occur in a Poisson manner in a particular state and the repair process will start immediately. The steady state probability vector of the number of customers in the system was evaluated as a quasi-birth and death (QBD) process, and the matrix geometric technique was used to derive the stationary condition. Some system performance measures are obtained. The effects of arrival rates, breakdown rates and repair rates on the mean number of customers and the influence of arrival rate on steady probabilities are shown through graphs.

Details

Title
An Analysis of Three Servers Markovian Multiple Vacation Queueing System with Servers Breakdown
Author
Karthick, V; Suvitha, V
Pages
1-8
Publication year
2023
Publication date
Jun 2023
Publisher
International Association of Engineers
ISSN
1992-9978
e-ISSN
1992-9986
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2823696902
Copyright
© 2023. This work is published under https://creativecommons.org/licenses/by-nc-nd/4.0/ (the“License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.