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A functional law of the iterated logarithm for multi-class queues with batch arrivals

Author

Listed:
  • Yongjiang Guo

    (Beijing University of Posts and Telecommunications)

  • Xiyang Hou

    (Huazhong University of Science and Technology)

  • Yunan Liu

    (North Carolina State University)

Abstract

A functional law of the iterated logarithm (LIL) and its corresponding LIL are established for a multiclass single-server queue with first come first served (FCFS) service discipline. The functional LIL and its LIL quantify the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. The functional LIL and LIL are established in three cases: underloaded, critically loaded and overloaded, for performance measures including the total workload, idle time, queue length, workload, busy time, departure and sojourn time processes. The proofs of the functional LIL and LIL are based on a strong approximation approach, which approximates discrete performance processes with reflected Brownian motions. Numerical examples are considered to provide insights on these limit results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:300:y:2021:i:1:d:10.1007_s10479-020-03864-6
    DOI: 10.1007/s10479-020-03864-6
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    References listed on IDEAS

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    1. 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.
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