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Computing the Matrix G of Multi-Dimensional Markov Chains of M/G/1 Type

Author

Listed:
  • Valeriy Naumov

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

  • Konstantin Samouylov

    (Institute of Computer Science and Telecommunications, RUDN University, 6 Miklukho-Maklaya St., Moscow 117198, Russia)

Abstract

We consider M d-M/G/1 processes, which are irreducible discrete-time Markov chains consisting of two components. The first component is a nonnegative integer vector, while the second component indicates the state (or phase) of the external environment. The level of a state is defined by the minimum value in its first component. The matrix G of the process represents the conditional probabilities that, starting from a given state of a certain level, the Markov chain will first reach a lower level in a specific state. This study aims to develop an effective algorithm for computing matrices G for M d-M/G/1 processes.

Suggested Citation

  • Valeriy Naumov & Konstantin Samouylov, 2025. "Computing the Matrix G of Multi-Dimensional Markov Chains of M/G/1 Type," Mathematics, MDPI, vol. 13(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1223-:d:1630378
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    References listed on IDEAS

    as
    1. Toshihisa Ozawa & Masahiro Kobayashi, 2018. "Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 351-403, December.
    2. Masakiyo Miyazawa, 2009. "Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 547-575, August.
    Full references (including those not matched with items on IDEAS)

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