Performance Characteristics of Discrete-Time Queue With Variant Working Vacations

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...

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Bibliographic Details
Published in:International journal of operations research and information systems 2020-04, Vol.11 (2), p.1-21
Main Authors: Laxmi, P Vijaya, Rajesh P
Format: Article
Language:English
Subjects:
Communication
Customer services
Customers
File servers
Information systems
Open access publishing
Operations research
Probability
Queuing theory
Random variables
Vacations
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Summary: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.
ISSN:1947-9328
1947-9336
DOI:10.4018/IJORIS.2020040101