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A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains

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  • Kim, Bara
  • Kim, Jeongsim

Abstract

Masuyama (2011) obtained the subexponential asymptotics of the stationary distribution of an M/G/1 type Markov chain under the assumption related to the periodic structure of G-matrix. In this note, we improve Masuyama’s result by showing that the subexponential asymptotics holds without the assumption related to the periodic structure of G-matrix.

Suggested Citation

  • Kim, Bara & Kim, Jeongsim, 2012. "A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains," European Journal of Operational Research, Elsevier, vol. 220(1), pages 132-134.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:1:p:132-134
    DOI: 10.1016/j.ejor.2012.01.016
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    References listed on IDEAS

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    1. Tetsuya Takine, 2004. "Geometric and Subexponential Asymptotics of Markov Chains of M / G /1 Type," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 624-648, August.
    2. Masuyama, Hiroyuki, 2011. "Subexponential asymptotics of the stationary distributions of M/G/1-type Markov chains," European Journal of Operational Research, Elsevier, vol. 213(3), pages 509-516, September.
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    Cited by:

    1. Hiroyuki Masuyama, 2022. "Subexponential asymptotics of asymptotically block-Toeplitz and upper block-Hessenberg Markov chains," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 175-217, October.
    2. Hiroyuki Masuyama, 2016. "A sufficient condition for the subexponential asymptotics of GI/G/1-type Markov chains with queueing applications," Annals of Operations Research, Springer, vol. 247(1), pages 65-95, December.

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