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Large deviations and long-time behavior of stochastic fluid queues with generalized fractional Brownian motion input

Author

Listed:
  • Sumith Reddy Anugu

    (Rice University)

  • Guodong Pang

    (Rice University)

Abstract

We study the large deviation behaviors of a stochastic fluid queue with an input being a generalized Riemann–Liouville (R–L) fractional Brownian motion (FBM), referred to as GFBM. The GFBM is a continuous mean-zero Gaussian process with non-stationary increments, extending the standard FBM with stationary increments. We first derive the large deviation principle for the GFBM by using the weak convergence approach. We then obtain the large deviation principle for the stochastic fluid queue with the GFBM as the input process as well as for an associated running maximum process. Finally, we study the long-time behavior of these two processes; in particular, we show that a steady-state distribution exists and derives the exact tail asymptotics using the aforementioned large deviation principle together with some maximal inequality and modulus of continuity estimates for the GFBM.

Suggested Citation

  • Sumith Reddy Anugu & Guodong Pang, 2023. "Large deviations and long-time behavior of stochastic fluid queues with generalized fractional Brownian motion input," Queueing Systems: Theory and Applications, Springer, vol. 105(1), pages 47-98, October.
    • Handle: RePEc:spr:queues:v:105:y:2023:i:1:d:10.1007_s11134-023-09889-5
    DOI: 10.1007/s11134-023-09889-5
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    References listed on IDEAS

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    1. Hüsler, J. & Piterbarg, V., 1999. "Extremes of a certain class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 257-271, October.
    2. Tomoyuki Ichiba & Guodong Pang & Murad S. Taqqu, 2022. "Path Properties of a Generalized Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 35(1), pages 550-574, March.
    3. Pipiras,Vladas & Taqqu,Murad S., 2017. "Long-Range Dependence and Self-Similarity," Cambridge Books, Cambridge University Press, number 9781107039469, December.
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