The Delay-Power Tradeoff of Low Complexity Cross-Layer Scheduling: When Lyapunov Meets Markov

Ultra-Reliable and Low-Latency Communications (URLLC) has attracted significant attention in the envisioned sixth-generation mobile systems (6G). The scheduling of back-logged queues in URLLC is a challenging issue worthy of researchers and engineers to study. Lyapunov optimization theory is regarded as a promising tool to design low-complexity scheduling strategies. However, it is difficult to analyze the tradeoff between the transmission delay and the transmission power with Lyapunov-based scheduling strategies. To solve this problem, we present an approach based on the Markov analysis in this paper. Specifically, we first develop one low-complexity scheduling strategy with heavy traffic based on the Lyapunov optimization theory. Then, uniform quantization is used to quantize the scheduling strategies so that the upper bound and lower bound of transmission delay can be calculated based on the Markov analysis. After that, we further extend this Markov analysis approach to estimate the transmission delay of another Lyapunov-based scheduling strategy with the consideration of a virtual power queue. Finally, simulation results not only verify our theoretical derivation but also demonstrate the potential of the Lyapunov-based scheduling strategies.