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Resource System with Losses in a Random Environment

Author

Listed:
  • Valeriy Naumov

    (Service Innovation Research Institute, Annankatu 8 A, 00120 Helsinki, Finland)

  • Konstantin Samouylov

    (Applied Informatics and Probability Department, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, 117198 Moscow, Russia
    Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilov St. 44-2, 119333 Moscow, Russia)

Abstract

The article deals with queueing systems with random resource requirements modeled as bivariate Markov jump processes. One of the process components describes the service system with limited resources. Another component represents a random environment that submits multi-class requests for resources to the service system. If the resource request is lost, then the state of the service system does not change. The change in the state of the environment interacting with the service system depends on whether the resource request has been lost. Thus, unlike in known models, the service system provides feedback to the environment in response to resource requests. By analyzing the properties of the system of integral equations for the stationary distribution of the corresponding random process, we obtain the conditions for the stationary distribution to have a product form. These conditions are expressed in the form of three systems of nonlinear equations. Several special cases are explained in detail.

Suggested Citation

  • Valeriy Naumov & Konstantin Samouylov, 2021. "Resource System with Losses in a Random Environment," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2685-:d:662528
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    References listed on IDEAS

    as
    1. Lovas, Attila & Rásonyi, Miklós, 2021. "Markov chains in random environment with applications in queuing theory and machine learning," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 294-326.
    2. Gely Basharin & Valeriy Naumov & Konstantin Samouylov, 2018. "On Markovian modelling of arrival processes," Statistical Papers, Springer, vol. 59(4), pages 1533-1540, December.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Ekaterina Pankratova & Svetlana Moiseeva & Mais Farkhadov, 2022. "Infinite-Server Resource Queueing Systems with Different Types of Markov-Modulated Poisson Process and Renewal Arrivals," Mathematics, MDPI, vol. 10(16), pages 1-16, August.

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