Scalable Distributed User-centric Cell-Free Transmission for Deterministic Communications

User-centric cell-free multiple-input multiple-output (MIMO) systems hold strong potential for enabling deterministic transmission by leveraging joint transmission and macro-diversity gains. However, realizing these gains entails challenges in computational complexity, fronthaul overhead and scalability, especially under stringent quality of service (QoS) requirements. In this paper, we propose a scalable hierarchical distributed scheduling framework based on safe reinforcement learning (SRL) to optimize the system throughput while ensuring user-specific latency bounds and delay violation probabilities constraints. We formulate the problem as a network constrained partially observable Markov game (NCPOMG) and propose a distributed algorithm where each access point (AP) locally determines the scheduling priorities of its serving users based on local observations. To further reduce computational and fronthaul overhead, AP performs local partial minimum mean square error (LP-MMSE) precoding based on the given scheduling priority. Simulation results demonstrate that the proposed framework significantly outperforms the earliest deadline first (EDF) strategy in delay guarantee, achieves approximately $99.99 \%$ deterministic transmission guarantee under the upper bound of 2 ms delay and $80 \%$ system load ratio, while reducing training and execution time by $77 \%$ relative to centralized scheduling, and maintains comparable QoS performance.