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Methods for Analysis of Queueing Models with Instantaneous and Delayed Feedbacks

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Information Technologies and Mathematical Modelling - Queueing Theory and Applications (ITMM 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 564))

Abstract

The new Markov models of multi-channel queueing systems with instantaneous and delayed feedback are proposed. In these models part of already serviced calls instantaneously feeds back to channel while the rest part either leaves the system or feeds back to channel after some delay in orbit. Behavior of already serviced calls is handled by randomized parameters. Both exact and asymptotic methods to calculate the quality of service (QoS) metrics of the proposed models are developed. Exact method is based on the system of balance equations (SBE) for steady-state probabilities of appropriate three dimensional Markov chain (3-D MC) while asymptotic method uses the new hierarchical space merging algorithm for 3-D MC. Results of numerical experiments are demonstrated.

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Author information

Authors and Affiliations

  1. Institute of Control Systems, ANAS, F. Agayev 9, AZ1141, Baku, Azerbaijan

    Agassi Melikov

  2. Institute of Information Technologies and Systems, NASU, Qlushkov Ave. 40, Kiev, 03680, Ukraine

    Leonid Ponomarenko

  3. Qafqaz University, H. Aliyev 120, AZ0101, Khirdalan, Baku, Azerbaijan

    Anar Rustamov

Authors
  1. Agassi Melikov
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  2. Leonid Ponomarenko
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  3. Anar Rustamov
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Corresponding author

Correspondence to Agassi Melikov .

Editor information

Editors and Affiliations

  1. Applied Mathematics and Computer Science, Belarusian State University, Minsk, Russia

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kemerovo State University, Anzhero-Sudzhensk, Russia

    Rafael Yakupov

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© 2015 Springer International Publishing Switzerland

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Melikov, A., Ponomarenko, L., Rustamov, A. (2015). Methods for Analysis of Queueing Models with Instantaneous and Delayed Feedbacks. In: Dudin, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2015. Communications in Computer and Information Science, vol 564. Springer, Cham. https://doi.org/10.1007/978-3-319-25861-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-25861-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25860-7

  • Online ISBN: 978-3-319-25861-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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