On a queue with interruptions and repeat or resumption of service
This paper presents an infinite-capacity queueing system with a single server where service rule is FIFO. A customer, on arrival to an idle server, is immediately taken for service; or else he joins the tail of the queue. The arrival of customers constitutes a MAP. During the service of a customer,...
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Published in | Nonlinear analysis Vol. 71; no. 12; pp. e1673 - e1683 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Ltd
15.12.2009
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Subjects | |
Online Access | Get full text |
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Summary: | This paper presents an infinite-capacity queueing system with a single server where service rule is FIFO. A customer, on arrival to an idle server, is immediately taken for service; or else he joins the tail of the queue. The arrival of customers constitutes a MAP. During the service of a customer, one or more interruptions may occur. It takes a random amount of time to clear the interruption. Interruption processes occur according to a Poisson process of rate
γ
and the duration of interruption is PH-distributed. When the duration of an interruption exceeds a threshold random variable (also PH-distributed), the customer whose service was interrupted has to undergo the service process right from the beginning on completion of the interruption; or else his service is resumed. We investigate this queueing system. Long-run system distribution is obtained under a stable regime. Several performance measures are evaluated. Numerical illustrations of the system behavior is also provided. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0362-546X 1873-5215 |
DOI: | 10.1016/j.na.2009.02.056 |