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International Conference on Distributed Computer and Communication Networks

DCCN 2019: Distributed Computer and Communication Networks pp 315–329Cite as

Heterogeneous Queueing System MAP/GI\(^{(n)}\)/\(\infty \) with Random Customers’ Capacities

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Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 11965))

Abstract

In this paper a model of a heterogeneous resource queueing system with a Markovian arrival process is considered. The customer accepted for servicing occupies random amount of resource with a given distribution function depending on the class of the customer and on the type of service it needs. At the end of the service, the customer leaves the system and releases the occupied resource. In this work, asymptotic formulas for calculating the main probability characteristics of the model, including the joint distribution functions of the customers number and the total resource amounts occupied by them, are obtained. Finally, the accuracy of the approximation is verified by using simulation.

The publication has been prepared with the support of the “RUDN University Program 5-100” (recipient E. Lisovskaya, mathematical model development). The reported study was funded by RFBR, project number 18-07-00576 (Y. Gaidamaka, simulation model development) and 17-07-00845 (Y. Gaidamaka, problem formulation and analysis) and the University of Pisa PRA 2018–2019 Research Project “CONCEPT Communication and Networking for vehicular Cyber-Physical systems” (recipient M. Pagano, simulation and numerical analysis).

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Author information

Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation

    Ekaterina Lisovskaya & Yuliya Gaidamaka

  2. Tomsk State University, 36 Lenina Avenue, Tomsk, 634050, Russian Federation

    Ekaterina Lisovskaya & Svetlana Moiseeva

  3. V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, Moscow, 117997, Russian Federation

    Ekaterina Pankratova

  4. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (FRC CSC RAS), 44-2 Vavilov Street, Moscow, 119333, Russian Federation

    Yuliya Gaidamaka

  5. Department of Information Engineering, University of Pisa, Via Caruso 16, 56122, Pisa, Italy

    Michele Pagano

Authors
  1. Ekaterina Lisovskaya
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  2. Ekaterina Pankratova
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  3. Yuliya Gaidamaka
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  4. Svetlana Moiseeva
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  5. Michele Pagano
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Corresponding author

Correspondence to Svetlana Moiseeva .

Editor information

Editors and Affiliations

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

    Vladimir M. Vishnevskiy

  2. Peoples' Friendship University of Russia, Moscow, Russia

    Konstantin E. Samouylov

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

    Dmitry V. Kozyrev

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Lisovskaya, E., Pankratova, E., Gaidamaka, Y., Moiseeva, S., Pagano, M. (2019). Heterogeneous Queueing System MAP/GI\(^{(n)}\)/\(\infty \) with Random Customers’ Capacities. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2019. Lecture Notes in Computer Science(), vol 11965. Springer, Cham. https://doi.org/10.1007/978-3-030-36614-8_24

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  • DOI: https://doi.org/10.1007/978-3-030-36614-8_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36613-1

  • Online ISBN: 978-3-030-36614-8

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