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Exact tail asymptotics for fluid models driven by an M/M/c queue

Author

Listed:
  • Wendi Li

    (Central South University)

  • Yuanyuan Liu

    (Central South University)

  • Yiqiang Q. Zhao

    (Carleton University)

Abstract

In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the M / M / c queue, which is a two-dimensional queueing system with a discrete phase and a continuous level. We extend the kernel method to study tail asymptotics of its stationary distribution, and a total of three types of exact tail asymptotics are identified from our study and reported in the paper.

Suggested Citation

  • Wendi Li & Yuanyuan Liu & Yiqiang Q. Zhao, 2019. "Exact tail asymptotics for fluid models driven by an M/M/c queue," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 319-346, April.
    • Handle: RePEc:spr:queues:v:91:y:2019:i:3:d:10.1007_s11134-019-09601-6
    DOI: 10.1007/s11134-019-09601-6
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    References listed on IDEAS

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    1. Masakiyo Miyazawa, 2009. "Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 547-575, August.
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    Cited by:

    1. 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.
    2. Yiqiang Q. Zhao, 2022. "The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 95-131, February.

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