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Analysis of the Polling System with Two Markovian Arrival Flows, Finite Buffers, Gated Service and Phase-Type Distribution of Service and Switching Times

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Book cover Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1605))

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Abstract

The polling system with two Markovian Arrival Flows, finite buffers, gated service discipline and Phase-Type (PH) distribution of service and switching times is considered. Stationary distribution of the continuous-time multi-dimensional Markov chain defining the current state of the server, number of customers in the buffers, the number of customers that should obtain service during the residual time of service of customers from various buffers and underlying processes of service or switching time and of arrival process is computed. Expressions for Laplace-Stieltjes transforms of distribution of waiting times of customers in both buffers are obtained. Numerical results giving some insight into performance of the system are presented.

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Acknowledgment

This paper has been supported by the RUDN University Strategic Academic Leadership Program.

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Authors and Affiliations

  1. Belarusian State University, 4 Nezavisimosti Avenue, 220030, Minsk, Belarus

    Alexander Dudin

  2. Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198, Moscow, Russia

    Alexander Dudin

  3. Francisk Skorina Gomel State University, 104 Sovetskaya str., 246019, Gomel, Belarus

    Yuliya Sinyugina

Authors
  1. Alexander Dudin
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  2. Yuliya Sinyugina
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Corresponding author

Correspondence to Alexander Dudin .

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Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Tomsk State University, Tomsk, Russia

    Alexander Moiseev

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Dudin, A., Sinyugina, Y. (2022). Analysis of the Polling System with Two Markovian Arrival Flows, Finite Buffers, Gated Service and Phase-Type Distribution of Service and Switching Times. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2021. Communications in Computer and Information Science, vol 1605. Springer, Cham. https://doi.org/10.1007/978-3-031-09331-9_1

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  • DOI: https://doi.org/10.1007/978-3-031-09331-9_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09330-2

  • Online ISBN: 978-3-031-09331-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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