On a single server queue with negative arrivals and request repeated



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Artalejo, Jesús R. and Gómez-Corral, Antonio (1999) On a single server queue with negative arrivals and request repeated. Journal of Applied Probability, 36 (3). pp. 907-918. ISSN 0021-9002

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Official URL: http://projecteuclid.org/euclid.jap/1032374643


There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Hanison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the Limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary 'truncated' system which can easily be evaluated with the help of a regenerative approach.

Item Type:Article
Uncontrolled Keywords:queueing theory; negative arrivals; linear request repeated; Fredholm integral equation; stable recursion schemes
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:15874
Deposited On:10 Jul 2012 08:33
Last Modified:06 Aug 2018 08:27

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