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Performance Characteristics of Discrete-Time Queue With Variant Working Vacations

Performance Characteristics of Discrete-Time Queue With Variant Working Vacations

P. Vijaya Laxmi, Rajesh P.
Copyright: © 2020 |Volume: 11 |Issue: 2 |Pages: 21
ISSN: 1947-9328|EISSN: 1947-9336|EISBN13: 9781799806547|DOI: 10.4018/IJORIS.2020040101
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MLA

Laxmi, P. Vijaya, and Rajesh P. "Performance Characteristics of Discrete-Time Queue With Variant Working Vacations." IJORIS vol.11, no.2 2020: pp.1-21. http://doi.org/10.4018/IJORIS.2020040101

APA

Laxmi, P. V. & Rajesh P. (2020). Performance Characteristics of Discrete-Time Queue With Variant Working Vacations. International Journal of Operations Research and Information Systems (IJORIS), 11(2), 1-21. http://doi.org/10.4018/IJORIS.2020040101

Chicago

Laxmi, P. Vijaya, and Rajesh P. "Performance Characteristics of Discrete-Time Queue With Variant Working Vacations," International Journal of Operations Research and Information Systems (IJORIS) 11, no.2: 1-21. http://doi.org/10.4018/IJORIS.2020040101

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Abstract

This article analyzes an infinite buffer discrete-time single server queueing system with variant working vacations in which customers arrive according to a geometric process. As soon as the system becomes empty, the server takes working vacations. The server will take a maximum number K of working vacations until either he finds at least on customer in the queue or the server has exhaustively taken all the vacations. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. The probability generating function of the steady-state probabilities and the closed form expressions of the system size when the server is in different states have been derived. In addition, some other performance measures, their monotonicity with respect to K and a cost model are presented to determine the optimal service rate during working vacation.