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1 results

  • A subgeometric convergence formula for finite-level M/G/1-type Markov chains: via a block-decomposition-friendly solution to the Poisson equation of the deviation matrix

  • Part of
  • Hiroyuki Masuyama, Yosuke Katsumata, Tatsuaki Kimura
  • Journal:
    Advances in Applied Probability / Volume 56 / Issue 2 / June 2024
    Published online by Cambridge University Press:
    01 December 2023, pp. 389-429
    Print publication:
    June 2024
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  • The purpose of this study is to present a subgeometric convergence formula for the stationary distribution of the finite-level M/G/1-type Markov chain when taking its infinite-level limit, where the upper boundary level goes to infinity. This study is carried out using the fundamental deviation matrix, which is a block-decomposition-friendly solution to the Poisson equation of the deviation matrix. The fundamental deviation matrix provides a difference formula for the respective stationary distributions of the finite-level chain and the corresponding infinite-level chain. The difference formula plays a crucial role in the derivation of the main result of this paper, and the main result is used, for example, to derive an asymptotic formula for the loss probability in the MAP/GI/1/N queue.