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A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic

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  • Delgado, Rosario

Abstract

We consider a family of non-deterministic fluid models that can be approximated under heavy traffic conditions by a multidimensional reflected fractional Brownian motion (rfBm). Specifically, we prove a heavy traffic limit theorem for multi-station fluid models with feedback and non-deterministic arrival process generated by a large enough number of heavy tailed ON/OFF sources, say N. Scaling in time by a factor r and in state space conveniently, and letting N and r approach infinity (in this order) we prove that the scaled immediate workload process converges in some sense to a rfBm.

Suggested Citation

  • Delgado, Rosario, 2007. "A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 188-201, February.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:2:p:188-201
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    Citations

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    Cited by:

    1. Hongshuai Dai, 2013. "Convergence in Law to Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 26(3), pages 676-696, September.
    2. Rosario Delgado, 2016. "A packet-switched network with On/Off sources and a fair bandwidth sharing policy: state space collapse and heavy-traffic," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(2), pages 461-479, June.
    3. Rosario Delgado, 2016. "A two-queue polling model with priority on one queue and heavy-tailed On/Off sources: a heavy-traffic limit," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 57-85, June.
    4. Lee Jeonghwa, 2021. "Generalized Bernoulli process with long-range dependence and fractional binomial distribution," Dependence Modeling, De Gruyter, vol. 9(1), pages 1-12, January.
    5. Hongshuai Dai, 2022. "Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 165-196, June.
    6. Wensheng Wang, 2024. "The Moduli of Continuity for Operator Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2097-2120, September.
    7. Lee, Jeonghwa, 2020. "Wavelet estimation in OFBM: Choosing scale parameter in different sampling methods and different parameter values," Statistics & Probability Letters, Elsevier, vol. 166(C).
    8. Lee Jeonghwa, 2021. "Generalized Bernoulli process: simulation, estimation, and application," Dependence Modeling, De Gruyter, vol. 9(1), pages 141-155, January.
    9. Lee, Chihoon, 2012. "Bounds on exponential moments of hitting times for reflected processes on the positive orthant," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1120-1128.

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