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

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.