Tail Delay Bound Analysis and Performance Optimization for Hierarchical SPMA via Stochastic Network Calculus

Ultra-reliable and low-latency communication scenarios impose stringent demands on the accuracy of delay distribution of the statistical priority-based multiple access (SPMA) protocol. For mission-critical services, the probabilistic guarantee of delay tail distribution directly dominates system reliability, while most existing SPMA studies focus on steady-state performance metrics, and the rigorous probabilistic analysis of delay tails remains insufficiently addressed.We propose a delay analysis and optimization framework for hierarchical priority SPMA via stochastic geometry and moment generating function-based stochastic network calculus (MGF-SNC), which addresses tail delay modeling difficulties through cross-layer unified modeling and native support for delay tail bound derivation. We first build a hierarchical Poisson bipolar SPMA network model, and derive the closed-form single burst success probability under composite fading and aggregated interference. Then, we characterize the arrival and service processes of SPMA, and rigorously derive analytical upper bounds on both the statistical delay violation probability (SDVP) and statistical delay (SD). We further establish optimization models for SDVP and SD minimization, and implement multi-parameter joint optimization via the genetic algorithm (GA). Numerical and simulation results verify that the proposed framework can accurately characterize the delayreliability relationship of SPMA, and effectively tighten the bounds of SDVP and SD. Furthermore, the proposed optimization scheme can reduce the system SDVP below 3×10⁻⁵ and cut the SD by more than 40%. This work provides theoretical support for optimizing the delay performance of SPMA protocols.