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Fundamental Matrix Of Transient Qbd Generator With Finite States And Level Dependent Transitions

Author

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  • YANG WOO SHIN

    (Department of Statistics, Changwon National University, Changwon, Gyeongnam 641-773, Korea)

Abstract

Fundamental matrix plays an important role in a finite-state Markov chain to find many characteristic values such as stationary distribution, expected amount of time spent in the transient state, absorption probabilities. In this paper, the fundamental matrix of the finite-state quasi-birth-and-death (QBD) process with absorbing state and level dependent transitions is considered. We show that each block component of the fundamental matrix can be expressed as a matrix product form and present an algorithm for computing the fundamental matrix. Some applications with numerical results are also presented.

Suggested Citation

  • Yang Woo Shin, 2009. "Fundamental Matrix Of Transient Qbd Generator With Finite States And Level Dependent Transitions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(05), pages 697-714.
    • Handle: RePEc:wsi:apjorx:v:26:y:2009:i:05:n:s0217595909002407
    DOI: 10.1142/S0217595909002407
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    Citations

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    Cited by:

    1. Antonio Gómez-Corral & Martín López-García & Maria Jesus Lopez-Herrero & Diana Taipe, 2020. "On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics," Mathematics, MDPI, vol. 8(10), pages 1-25, October.
    2. Shin, Yang Woo, 2015. "Algorithmic approach to Markovian multi-server retrial queues with vacations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 287-297.
    3. Yang Woo Shin & Dug Hee Moon, 2014. "M/M/c Retrial Queue with Multiclass of Customers," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 931-949, December.
    4. Niek Baer & Ahmad Al Hanbali & Richard J. Boucherie & Jan-Kees van Ommeren, 2022. "A successive censoring algorithm for a system of connected LDQBD-processes," Annals of Operations Research, Springer, vol. 310(2), pages 389-410, March.
    5. Hiroyuki Masuyama, 2019. "A sequential update algorithm for computing the stationary distribution vector in upper block-Hessenberg Markov chains," Queueing Systems: Theory and Applications, Springer, vol. 92(1), pages 173-200, June.

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