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

Chang Feng (), John J. Hasenbein () and Guodong Pang ()
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Chang Feng: The University of Texas at Austin
John J. Hasenbein: The University of Texas at Austin
Guodong Pang: Rice University

Queueing Systems: Theory and Applications, 2025, vol. 109, issue 2, No 1, 37 pages

Abstract: 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.

Keywords: GI/GI/1+GI queues; Near-heavy-traffic regime (nearly critically loaded regime); Sample-path moderate deviation principles; Exponential tightness; 60F10; 60K25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11134-025-09939-0

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