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Sample-path moderate deviation principle for GI/GI/1+GI queues in the nearly critically loaded regime

Author

Listed:
  • Chang Feng

    (The University of Texas at Austin)

  • John J. Hasenbein

    (The University of Texas at Austin)

  • Guodong Pang

    (Rice University)

Abstract

This paper establishes sample-path moderate deviation principles (MDP) for GI/GI/1+GI queues in the nearly critically loaded regime (or near-heavy-traffic regime). The processes of interest including queue-length process and offered waiting time process are scaled appropriately, with the space scaled in between the order of the time scaling and its square root. The rate functions in the sample-path MDPs for these processes can be explicitly expressed. We employ the method of exponential tightness, exponential equivalence and the contraction principle in large deviation theory and apply to these MDP-scaled processes.

Suggested Citation

  • Chang Feng & John J. Hasenbein & Guodong Pang, 2025. "Sample-path moderate deviation principle for GI/GI/1+GI queues in the nearly critically loaded regime," Queueing Systems: Theory and Applications, Springer, vol. 109(2), pages 1-37, June.
    • Handle: RePEc:spr:queues:v:109:y:2025:i:2:d:10.1007_s11134-025-09939-0
    DOI: 10.1007/s11134-025-09939-0
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    References listed on IDEAS

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    1. Rami Atar & Amarjit Budhiraja & Paul Dupuis & Ruoyu Wu, 2022. "Large Deviations for the Single-Server Queue and the Reneging Paradox," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 232-258, February.
    2. J. E. Reed & Amy R. Ward, 2008. "Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 606-644, August.
    3. Anup Biswas, 2014. "Risk-Sensitive Control for the Multiclass Many-Server Queues in the Moderate Deviation Regime," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 908-929, August.
    4. Chihoon Lee & Amy R. Ward & Heng-Qing Ye, 2020. "Stationary distribution convergence of the offered waiting processes for $$GI/GI/1+GI$$GI/GI/1+GI queues in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 147-173, February.
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