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Insensitivity in Stochastic Models

In: Queueing Networks

Author

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  • P. G. Taylor

    (University of Melbourne)

Abstract

A stochastic model is said to be insensitive if its stationary distribution depends on one or more of its constituent lifetime distributions only through the mean. Insensitivity is usually associated with partial balance in the corresponding Markovianmodel when all lifetimes are taken to be exponential, and a product-form stationary distribution of the Markov chain, constructed by supplementing the state by information on the progress of generally-distributed lifetimes.

Suggested Citation

  • P. G. Taylor, 2011. "Insensitivity in Stochastic Models," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 0, pages 121-140, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-6472-4_3
    DOI: 10.1007/978-1-4419-6472-4_3
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    Cited by:

    1. Tsai, Eline R. & Demirtas, Derya & Tintu, Andrei N. & de Jonge, Robert & de Rijke, Yolanda B. & Boucherie, Richard J., 2023. "Design of fork-join networks of First-In-First-Out and infinite-server queues applied to clinical chemistry laboratories," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1101-1117.
    2. Nico Dijk & Barteld Schilstra, 2022. "On two product form modifications for finite overflow systems," Annals of Operations Research, Springer, vol. 310(2), pages 519-549, March.
    3. Amir Rastpour & Armann Ingolfsson & Bora Kolfal, 2020. "Modeling Yellow and Red Alert Durations for Ambulance Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(8), pages 1972-1991, August.
    4. Richard J. Boucherie, 2022. "Norton’s theorem and insensitivity," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 181-183, April.

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