Queueing Systems

, Volume 39, Issue 2–3, pp 157–182 | Cite as

Analysis of Markov Multiserver Retrial Queues with Negative Arrivals

  • Vladimir V. Anisimov
  • Jesus R. Artalejo
Article

Abstract

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.

retrial queueing systems negative arrivals averaging principle matrix–analytic methods switching process 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Vladimir V. Anisimov
    • 1
    • 2
  • Jesus R. Artalejo
    • 3
  1. 1.Department of Industrial EngineeringBilkent University, BilkentAnkaraTurkey
  2. 2.Applied Statistics DepartmentKiev UniversityKiev-17Ukraine
  3. 3.Department of Statistics and Operations ResearchComplutense University of MadridMadridSpain

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