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

Abstract 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.

• Publication year

  2023

• Venue

  Advances in Applied Probability

• Publication date

  2023-12-01

• Fields of study

  Not labeled

• Identifiers
  DOI 10.1017/apr.2023.39
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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