Lyapunov-Based Completion-Aware Scheduling for PDU Set-Based Real-Time XR Traffic

Real-time extended reality (XR) services impose stringent throughput, latency, and reliability requirements. An XR media unit is commonly segmented into a protocol data unit (PDU) set that is useful only when all required PDUs are delivered within its delay budget. Existing PDU set-aware medium access control (MAC) schedulers generally prioritize transmissions according to urgency or progress, without explicitly accounting for whether a PDU set can still be completed on time. In this paper, we propose a Lyapunov-based completion-aware MAC scheduler that jointly captures the set-level completion dependency, deadline urgency, and completion feasibility of each head-of-line PDU set. Long-term quality-of-service (QoS) requirements are represented through virtual debt queues, and resources are allocated according to their marginal contribution to the timely-completion probability of each head-of-line PDU set. These components are integrated into a drift-plus-penalty scheduling metric that balances long-term reliability requirements against current completion opportunities. System-level simulations demonstrate that the proposed scheduler improves PDU set delivery reliability and lower-tail performance under resource contention, while providing robust performance across heterogeneous traffic demands and network conditions.