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An Algorithm for Asymptotic Mean and Variance for Markov Renewal Process of M/G/1 Type with Finite Level

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  • Yang Woo Shin

    (Changwon National University)

Abstract

The Markov renewal process (MRP) of M/G/1 type has been used for modeling many complex queueing systems with correlated arrivals and the special types of transitions of the MRP process corresponds to the departures from the queueing system. It can be seen from the central limit theorem for regenerative process that the distribution of the number of transitions of MRP is asymptotically normal. Thus, the asymptotic mean and variance of the number of transitions of MRP can be used to estimate the number of departures in the queueing system modelled by MRP. The aim of this paper is to present an algorithm for computing the asymptotic mean and variance for the number of level-down-transitions in a Markov renewal process of M/G/1 type with finite level. The results are applied to the queueing system with finite buffer and correlated arrivals.

Suggested Citation

  • Yang Woo Shin, 2022. "An Algorithm for Asymptotic Mean and Variance for Markov Renewal Process of M/G/1 Type with Finite Level," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 195-212, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09846-w
    DOI: 10.1007/s11009-021-09846-w
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    References listed on IDEAS

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    1. Barış Tan, 2013. "Modeling and Analysis of Output Variability in Discrete Material Flow Production Systems," International Series in Operations Research & Management Science, in: J. MacGregor Smith & Barış Tan (ed.), Handbook of Stochastic Models and Analysis of Manufacturing System Operations, edition 127, chapter 0, pages 287-311, Springer.
    2. Barış Tan, 2000. "Asymptotic variance rate of the output in production lines with finite buffers," Annals of Operations Research, Springer, vol. 93(1), pages 385-403, January.
    3. Svenja Lagershausen & Bariş Tan, 2015. "On the Exact Inter-departure, Inter-start, and Cycle Time Distribution of Closed Queueing Networks Subject to Blocking," IISE Transactions, Taylor & Francis Journals, vol. 47(7), pages 673-692, July.
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