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Approximate Description of Dynamics of a Closed Queueing Network Including Multi-servers

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Distributed Computer and Communication Networks (DCCN 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 601))

Abstract

We investigate a closed network consisting of two multi-servers with n customers. Service requirements of customers at a server have a common cumulative distribution function. The state of the network is described by the following state parameters: for each multi-server and for the queue empirical measures of the age of customers being serviced/waiting in the queue multiplied by \(n^{-1}\). The approximation of a single multi-server dynamics is currently studied by famous scientists H. Kaspi, K. Ramanan, W. Whitt et al. We find approximation for a network, but only in discrete time.

A motivation for studying such systems is that they arise as models of computer data systems and call centers.

This work was supported by RFBR grant No. 14-01-00319 “Asymptotic analysis of queueing systems and nets”.

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Notes

  1. 1.

    They describe queues after customers leave them and go to the emptied servers.

  2. 2.

    Even starting from an arbitrary k.

References

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Authors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, Moscow, Russia

    Svetlana Anulova

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  1. Svetlana Anulova
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Correspondence to Svetlana Anulova .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sc, Russian Academy of Sciences V.A. Trapeznikov Institute of Control Sc, Moscow, Russia

    Vladimir Vishnevsky

  2. V.A. Trapeznikov Inst. of Control Scienc, Russian Academy of Sciences V.A. Trapeznikov Inst. of Control Scienc, Moscow, Russia

    Dmitry Kozyrev

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Anulova, S. (2016). Approximate Description of Dynamics of a Closed Queueing Network Including Multi-servers. In: Vishnevsky, V., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2015. Communications in Computer and Information Science, vol 601. Springer, Cham. https://doi.org/10.1007/978-3-319-30843-2_19

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  • DOI: https://doi.org/10.1007/978-3-319-30843-2_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30842-5

  • Online ISBN: 978-3-319-30843-2

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