On a queue with interruptions and repeat or resumption of service

• Published in: Nonlinear analysis Vol. 71; no. 12; pp. e1673 - e1683
• Main Authors: Krishnamoorthy, A., Pramod, P.K., Deepak, T.G.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.12.2009
• Subjects: Arrivals; Customer satisfaction; Illustrations; Interruption; Markovian arrival process (MAP); Matrix analytic methods; Nonlinearity; Performance evaluation; PH distribution; Queues; Servers; Threshold random variable; Markovian arrival process (MAP); Threshold random variable; Matrix analytic methods; PH distribution; primary
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2009.02.056

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.