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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Chang Feng,
  • John J. Hasenbein,
  • Guodong Pang

摘要

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.