Analysis of Markov multiserver retrial queues with negative arrivals



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Artalejo, Jesús R. and Anisimov, Vladimir V. (2001) Analysis of Markov multiserver retrial queues with negative arrivals. Queueing Systems, 39 (2-3). pp. 157-182. ISSN 0257-0130

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Negative arrivals are used as a control mechanism in many telecommunication and computer networks. In the paper we analyze multiserver retrial queues; i.e., any customer finding all servers busy upon arrival must leave the service area and re-apply for service after some random time. The control mechanism is such that, whenever the service facility is full occupied, an exponential timer is activated. If the timer expires and the service facility remains full, then a random batch of customers, which are stored at the retrial pool, are automatically removed. This model extends the existing literature, which only deals
with a single server case and individual removals. Two different approaches are considered. For the stable case, the matrix–analytic formalism is used to study the joint distribution of the service facility and the retrial pool. The approximation by more simple infinite retrial model is also proved. In the overloading case we study the transient behaviour of the trajectory of the suitably normalized retrial queue and the long-run behaviour of the number of busy servers. The method of investigation in this case is based on the averaging principle for switching processes.

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This research was supported in part by DGES98-0837 and the European Commission through INTAS Project 96-0828

Uncontrolled Keywords:Retrial queueing systems, Negative arrivals, Averaging principle, Matrix–analytic methods, Switching process
Subjects:Sciences > Mathematics > Operations research
ID Code:15838
Deposited On:05 Jul 2012 09:50
Last Modified:03 Aug 2018 10:51

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