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A queueing system with negative claims and a bunker for superseded claims in discrete time

  • Non-Classical Models of the Queuing Theory
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Abstract

We consider a discrete time single-line queueing system with independent geometric streams of regular and negative claims, infinite buffer, and geometric service. A negative claim pushes a regular claim out of the buffer queue and moves it to a bunker of infinite capacity. If the buffer is empty, a negative claim leaves the system without any effect. After servicing a claim, the system receives the next claim from the buffer, if it is not empty, or from the bunker. We obtain relations that allow computing stationary distributions for queues in the buffer and the bunker.

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Authors and Affiliations

  1. Institute of Informatics Problems, Russian Academy of Sciences, Moscow, Russia

    A. V. Pechinkin

  2. Peoples Friendship University, Moscow, Russia

    R. V. Razumchik

Authors
  1. A. V. Pechinkin
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  2. R. V. Razumchik
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Additional information

Original Russian Text © A.V. Pechinkin, R.V. Razumchik, 2009, published in Avtomatika i Telemekhanika, 2009, No. 12, pp. 109–120.

This work was supported by the by the Russian Foundation for Basic Research, projects nos. 08-07-00152 and 09-07-12032.

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Pechinkin, A.V., Razumchik, R.V. A queueing system with negative claims and a bunker for superseded claims in discrete time. Autom Remote Control 70, 2039–2049 (2009). https://doi.org/10.1134/S000511790912011X

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  • DOI: https://doi.org/10.1134/S000511790912011X

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