A Tractable Approach for Queueing Analysis on Buffer-Aware Scheduling

Low-latency communication has recently attracted considerable attention owing to its potential of enabling delay-sensitive services in next-generation industrial cyber-physical systems. To achieve target average or maximum delay given random arrivals and time-varying channels, buffer-aware scheduling is expected to play a vital role. Evaluating and optimizing buffer-aware scheduling relies on its queueing analysis, while existing tools are not sufficiently tractable. Particularly, Markov chain and Monte-Carlo based approaches are computationally intensive, while large deviation theory (LDT) and extreme value theory (EVT) fail in providing satisfactory accuracy in the small-queue-length (SQL) regime. To tackle these challenges, a tractable yet accurate queueing analysis is presented by judiciously bridging Markovian analysis for the computationally manageable SQL regime and LDT/EVT for large-queue-length (LQL) regime where approximation error diminishes asymptotically. Specifically, we leverage censored Markov chain augmentation to approximate the original one in the SQL regime, while a piecewise approach is conceived to apply LDT/EVT across various queue-length intervals with different scheduling parameters. Furthermore, we derive closed-form bounds on approximation errors, validating the rigor and accuracy of our approach. As a case study, the approach is applied to analytically analyze a Lyapunov-drift-based cross-layer scheduling for wireless transmissions. Numerical results demonstrate its potential in balancing accuracy and complexity.