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Stochastic Fluid Models with Upward Jumps and Phase Transitions

Author

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  • Hédi Nabli

    (Universty of Sfax)

  • Itidel Abdallah

    (Universty of Sfax
    University of Littoral Côte d’Opale)

Abstract

In this paper, we are interested in stochastic fluid flow model with upward jumps at level zero and instantaneous phase transitions at jumps epochs. This mathematical model is governed by a non-homogeneous differential system with specific boundary conditions. We derive three algorithms for computing explicitly the fluid level distribution. We study the general case of the model, the case where the phase process conserves its state when the fluid jumps, and a special case where the phase process transits to a deterministic fixed state at jumps epochs. Numerical results are carried out to illustrate the numerical stability and the advantages in computational time for the proposed approaches.

Suggested Citation

  • Hédi Nabli & Itidel Abdallah, 2023. "Stochastic Fluid Models with Upward Jumps and Phase Transitions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09982-5
    DOI: 10.1007/s11009-023-09982-5
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    References listed on IDEAS

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    1. V. Ramaswami, 2006. "Passage Times in Fluid Models with Application to Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 497-515, December.
    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. Barron, Yonit, 2016. "Clearing control policies for MAP inventory process with lost sales," European Journal of Operational Research, Elsevier, vol. 251(2), pages 495-508.
    4. Eleonora Deiana & Guy Latouche & Marie-Ange Remiche, 2021. "Fluid Flow Model for Energy-Aware Server Performance Evaluation," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 801-821, September.
    5. Hédi Nabli, 2022. "Stochastic Fluid Models with Positive Jumps at Level Zero," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 289-308, March.
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