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Interconnections of Markov chains and quasi-reversible queuing networks

Author

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  • Walrand, Jean
  • Varaiya, Pravin

Abstract

A quasi-reversible queue can be associated with certain type of transactions of a Markov chain. It is shown that if Markov chains are coupled in a certain way, then to the resulting chain be associated a queuing network which is itself quasi-reversible and the stationary distribution of the chain takes the product form. The product form for mixed networks is derived from the result for open networks.

Suggested Citation

  • Walrand, Jean & Varaiya, Pravin, 1980. "Interconnections of Markov chains and quasi-reversible queuing networks," Stochastic Processes and their Applications, Elsevier, vol. 10(2), pages 209-219, September.
    • Handle: RePEc:eee:spapps:v:10:y:1980:i:2:p:209-219
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    Citations

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    Cited by:

    1. Boucherie, R.J., 1990. "Aggregation of stochastic processes," Serie Research Memoranda 0077, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Xiuli Chao & Masakiyo Miyazawa, 1998. "On Quasi-Reversibility and Local Balance: An Alternative Derivation of the Product-Form Results," Operations Research, INFORMS, vol. 46(6), pages 927-933, December.
    3. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    4. Boucherie, R.J. & Dijk, N.M. van, 1991. "A generalization of Norton's theorem," Serie Research Memoranda 0061, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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