Lyapunov-Based Cross-Layer Transmission Control for Finite-Blocklength URLLC Systems with Deadline-Constrained Queues

Ultra-Reliable Low-Latency Communication (URLLC) systems require extremely reliable packet delivery under stringent latency constraints, particularly in mission-critical wireless applications such as industrial automation, autonomous transportation, and intelligent control systems. In such systems, communication reliability is jointly influenced by finite-blocklength decoding behavior, stochastic wireless channel variations, queue evolution, and packet deadline violations. This paper develops a Lyapunov-based cross-layer transmission control framework for finite-blocklength URLLC systems with deadline-constrained queues and stochastic traffic arrivals. The proposed method jointly models short-packet communication reliability, queue dynamics, packet expiration, and adaptive transmission parameter selection within a unified mathematical formulation. An end-to-end (E2E) reliability metric incorporating both physical-layer (PHY) decoding failures and queue-induced deadline violations is introduced. In order to satisfy long-term reliability and power constraints while preserving queue stability, virtual queues are constructed and integrated into a Lyapunov drift-plus-penalty optimization framework. Based on the proposed formulation, an online transmission control algorithm is developed for adaptive selection of transmission blocklength, coding rate, and transmit power according to instantaneous queue and wireless channel conditions. Unlike reinforcement-learning-based methods, the proposed framework does not require offline training or prior statistical knowledge of traffic and channel distributions. The analysis establishes bounded real-queue occupancy under capped admissions and deadline expiration, and shows that mean-rate stability of the virtual queues implies the corresponding surrogate-risk and power constraints. Classical Lyapunov scaling is discussed as a conditional benchmark rather than an established optimality guarantee for the implemented urgency-weighted controller. Simulation results show that the proposed framework reduces time-average transmit power by approximately 33.0% relative to Adaptive-FBL, 42.3% relative to EC-FBL, 46.7% relative to the simplified Lyapunov baseline, and 71.6% relative to fixed transmission, while maintaining packet-level reliability, delay, and queueing performance close to the adaptive benchmarks. Simulation results show that the proposed approach achieves a favorable balance between reliability, latency, and energy consumption across different traffic conditions.