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Networks of interacting stochastic fluid models with infinite and finite buffers

Author

Listed:
  • Nikki Sonenberg

    (The University of Melbourne)

  • Peter G. Taylor

    (The University of Melbourne)

Abstract

Stochastic fluid models have been widely used to model the level of a resource that changes over time, where the rate of variation depends on the state of some continuous-time Markov process. Latouche and Taylor (Queueing Syst 63:109–129, 2009) introduced an approach, using matrix analytic methods and the reduced load approximation for loss networks, to analyse networks of fluid models all driven by the same modulating process where the buffers are infinite. We extend the method to networks involving finite buffer models and illustrate the approach by deriving performance measures for a simple network as characteristics such as buffer size are varied. Our results provide insight into the situations where the infinite buffer model is a reasonable approximation to the finite buffer model.

Suggested Citation

  • Nikki Sonenberg & Peter G. Taylor, 2019. "Networks of interacting stochastic fluid models with infinite and finite buffers," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 293-322, August.
    • Handle: RePEc:spr:queues:v:92:y:2019:i:3:d:10.1007_s11134-019-09619-w
    DOI: 10.1007/s11134-019-09619-w
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    References listed on IDEAS

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    1. Barbara Margolius & Małgorzata M. O’Reilly, 2016. "The analysis of cyclic stochastic fluid flows with time-varying transition rates," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 43-73, February.
    2. Samuelson, Aviva & Haigh, Andrew & O'Reilly, Małgorzata M. & Bean, Nigel G., 2017. "Stochastic model for maintenance in continuously deteriorating systems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1169-1179.
    3. Bean, Nigel G. & O’Reilly, Małgorzata M., 2014. "The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process, which is a stochastic fluid model itself," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1741-1772.
    4. Bean, Nigel G. & O'Reilly, Malgorzata M. & Taylor, Peter G., 2005. "Hitting probabilities and hitting times for stochastic fluid flows," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1530-1556, September.
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