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Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback

Author

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  • Yongjiang Guo

    (Beijing University of Posts and Telecommunications)

  • Yunan Liu

    (North Carolina State University)

  • Renhu Pei

    (Beijing University of Posts and Telecommunications)

Abstract

A functional law of the iterated logarithm (FLIL) and its corresponding law of the iterated logarithm (LIL) are established for a multi-server queue with batch arrivals and customer feedback. The FLIL and LIL, which quantify the magnitude of asymptotic fluctuations of the stochastic processes around their mean values, are developed in three cases: underloaded, critically loaded and overloaded, for five performance measures: queue length, workload, busy time, idle time and departure process. Both FLIL and LIL are proved using an approach based on strong approximations.

Suggested Citation

  • Yongjiang Guo & Yunan Liu & Renhu Pei, 2018. "Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback," Annals of Operations Research, Springer, vol. 264(1), pages 157-191, May.
    • Handle: RePEc:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2529-9
    DOI: 10.1007/s10479-017-2529-9
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    References listed on IDEAS

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    1. Yongjiang Guo & Xiyang Hou & Yunan Liu, 2021. "A functional law of the iterated logarithm for multi-class queues with batch arrivals," Annals of Operations Research, Springer, vol. 300(1), pages 51-77, May.

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