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Heuristic Solution for the Optimal Thresholds in a Controllable Multi-server Heterogeneous Queueing System Without Preemption

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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

As it known the optimal policy which minimizes the long-run average cost per unit of time in a multi-server queueing system with heterogeneous servers without preemption has a threshold structure. It means that the slower server must be activated whenever all faster servers are busy and the number of customers in the queue exceeds some specified for this server threshold level. The optimal thresholds can be evaluated using the Howard iteration algorithm or by minimizing the function of the average cost which can be obtained in closed form as a function of unknown threshold levels. The both cases have sufficient restrictions on dimensionality of the model. In present paper we provide a heuristic method to derive expressions for the optimal threshold levels in explicit form as functions of system parameters like service intensities, usage and holding costs for an arbitrary number of servers. The proposed method is based on the fitting of the boundary planes between the areas where the optimal threshold takes a certain value.

D. Efrosinin—This work was funded by the Russian Foundation for Basic Research (RFBR), Project No 15-08-08677-a.

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Author information

Authors and Affiliations

  1. Johannes Kepler University Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Dmitry Efrosinin

  2. Institute of Control Sciences, RAS, Profsoyuznaya street 65, 117997, Moscow, Russia

    Dmitry Efrosinin

  3. Gubkin Russian State University of Oil and Gas, Leninskiy prospect 65, 119991, Moscow, Russia

    Vladimir Rykov

Authors
  1. Dmitry Efrosinin
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  2. Vladimir Rykov
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Corresponding author

Correspondence to Dmitry Efrosinin .

Editor information

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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Efrosinin, D., Rykov, V. (2016). Heuristic Solution for the Optimal Thresholds in a Controllable Multi-server Heterogeneous Queueing System Without Preemption. 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_25

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  • DOI: https://doi.org/10.1007/978-3-319-30843-2_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30842-5

  • Online ISBN: 978-3-319-30843-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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