Probabilistic Analysis of Delay and Reliability Violations With Jitter Sensitivity in Finite Blocklength Cell-Free Massive MIMO

Abstract

In the sixth generation (6G) mobile networks, extreme ultra-reliable and low-latency communications (xURLLC) demand deterministic performance to guarantee absolute service in mission-critical applications. Nevertheless, most existing studies rely on average reliability metrics, fixed service configurations, or upper-bound approximations, with limited attention to tail behavior. Consequently, we establish an integrated framework that explicitly incorporates physical-layer reliability fluctuations into delay tail characterization in grant-free uplink cell-free massive multiple-input multiple-output (CF-mMIMO) systems. Specifically, we approximate the instantaneous SINR distribution and derive the corresponding decoding error probability (DEP) distribution under finite blocklength and imperfect channel state information, from which the reliability violation probability (RVP) is introduced as a reliability metric capturing extreme reliability events. Then, we embed this stochastic reliability into retransmission and develop a generic Markov queuing model to quantify the over-the-air delay distribution, delay violation probability (DVP), and jitter. Based on these metrics, we formulate the jitter minimization problem under individual RVP and DVP constraints and address it with a multi-agent twin delayed deep deterministic policy gradient (MATD3) resource allocation algorithm. Simulation results validate the theoretical framework and the proposed algorithm, supporting statistically deterministic performance in 6G xURLLC scenarios.