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International Conference on Distributed Computer and Communication Networks

DCCN 2016: Distributed Computer and Communication Networks pp 132–144Cite as

Optimal Control of M(t)/M/K Queues with Homogeneous and Heterogeneous Servers

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 678))

Abstract

The paper deals with a multi-server controllable queueing system M(t)/M/K with time-dependent and, in particular, with periodic arrival rates. The models with homogeneous and heterogeneous servers are of interest. In latter case the fastest free server allocation mechanism is assumed and the preemption is allowed. The control problem consists in evaluation of the optimal number of servers during some specified stages and is solved by finite horizon dynamic programming approach. To calculate the transient solutions we use a forth-order Runge-Kutta method for the system with a truncated queue length. The results are compared with corresponding queues operating in a stationary regime. It is shown that the optimal control policies are also time dependent and periodic as arrival rates and heterogeneous systems are superior in performance comparing to the homogeneous ones.

D. Efrosinin—This work was funded by the Russian Foundation for Basic Research, Project No. 16-37-60072 mol_a_dk. The reported study was funded within the Agreement No. 02.a03.21.0008 dated 24.11.2016 between the Ministry of Education and Science of the Russian Federation and RUDN University.

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References

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Author information

Authors and Affiliations

  1. Institute of Control Sciences, Profsoyuznaya str., 65, 117997, Moscow, Russia

    Dmitry Efrosinin

  2. RUDN University, Miklukho-Maklaya str., 6, 117198, Moscow, Russia

    Dmitry Efrosinin

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

    Michael Feichtenschlager

Authors
  1. Dmitry Efrosinin
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  2. Michael Feichtenschlager
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Corresponding author

Correspondence to Dmitry Efrosinin .

Editor information

Editors and Affiliations

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

    Vladimir M. Vishnevskiy

  2. RUDN University , Moscow, Russia

    Konstantin E. Samouylov

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

    Dmitry V. Kozyrev

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© 2016 Springer International Publishing AG

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Efrosinin, D., Feichtenschlager, M. (2016). Optimal Control of M(t)/M/K Queues with Homogeneous and Heterogeneous Servers. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2016. Communications in Computer and Information Science, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-319-51917-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-51917-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51916-6

  • Online ISBN: 978-3-319-51917-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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