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Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates

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Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13766 ))

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Abstract

A two-class single-server retrial system with Poisson inputs is considered. In this system, unlike conventional retrial systems, each new ith class customer joins the ‘end’ of a virtual ith class orbit, and the ‘oldest’ customer from each orbit is only allowed to make an attempt to occupy server after a class-dependent exponential retrial time. Moreover, the server is assumed to be not reliable, and a customer whose service is interrupted joins the ‘top’ of class-i orbit queue. Thus FIFO discipline is applied in both orbits. Using regenerative methodology and Markov Chain approach we derive stability conditions of this system relying on analysis for less-complicated model with reliable server. Obtained conditions are verified by simulation. Additionally, we analyze a controllable variant of the main model operating under a \(c\mu \)-rule. For that case the system becomes less stable comparing to the non-controllable counterpart.

The research of RN was prepared with the support of Russian Science Foundation according to the research project No. 21-71-10135 https://rscf.ru/en/project/21-71-10135/. The research of EM was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement № 075-15-2022-284.

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Authors and Affiliations

  1. IAMR Karelian Research Centre RAS, Petrozavodsk, Russia

    Ruslana Nekrasova & Evsey Morozov

  2. Petrozavodsk State University, Petrozavodsk, Russia

    Ruslana Nekrasova & Evsey Morozov

  3. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, 119991, Russia

    Evsey Morozov

  4. Johannes Kepler University, Linz, Austria

    Dmitry Efrosinin

  5. Peoples Frienship University of Russia, Moscow, Russia

    Dmitry Efrosinin

Authors
  1. Ruslana Nekrasova
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  2. Evsey Morozov
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  3. Dmitry Efrosinin
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Corresponding author

Correspondence to Ruslana Nekrasova .

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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Nekrasova, R., Morozov, E., Efrosinin, D. (2022). Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science, vol 13766 . Springer, Cham. https://doi.org/10.1007/978-3-031-23207-7_23

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  • DOI: https://doi.org/10.1007/978-3-031-23207-7_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23206-0

  • Online ISBN: 978-3-031-23207-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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