Queueing Analysis of GPU-Based Inference Servers with Dynamic Batching: A Closed-Form Characterization

GPU-accelerated computing is a key technology to realize high-speed inference servers using deep neural networks (DNNs). An important characteristic of GPU-based inference is that the computational efficiency, in terms of the processing speed and energy consumption, drastically increases by processing multiple jobs together in a batch. In this paper, we formulate GPU-based inference servers as a batch service queueing model with batch-size dependent processing times. We first show that the energy efficiency of the server monotonically increases with the arrival rate of inference jobs, which suggests that it is energy-efficient to operate the inference server under a utilization level as high as possible within a latency requirement of inference jobs. We then derive a closed-form upper bound for the mean latency, which provides a simple characterization of the latency performance. Through simulation and numerical experiments, we show that the exact value of the mean latency is well approximated by this upper bound. We further compare this upper bound with the latency curve measured in real implementation of GPU-based inference servers and we show that the real performance curve is well explained by the derived simple formula.