Artificial Intelligence Constrained Reinforcement Learning for Radiotherapy Beam Scheduling Under Variable Linear Accelerator Downtime Telemetry: A computed Evaluation of Healthcare Treatment Delay Equity

Linear accelerator downtime disrupts radiotherapy beam scheduling and can distribute treatment delays unevenly across patient groups. The scheduling problem is cast as a constrained Markov decision process in which the state includes observed downtime indicators, the action assigns waiting patients to available beam slots, and the constraint bounds the probability that any protected patient subgroup exceeds a clinically meaningful delay threshold. A Lagrangian relaxation with a per-subgroup multiplier yields a tractable policy improvement step, and the resulting algorithm is analysed for feasibility and convergence under a declared variance structure. Because no observational scheduling data were available, the evaluation is a design study: the operating characteristics of the before-after-control-impact estimator used to appraise the policy are characterised under a between-cluster standard deviation of 6.0, a residual standard deviation of 4.5 and an intraclass correlation of 0.64, with 2000 replications per design cell across 8, 16, 24 and 32 clusters and effects of 3, 5 and 8 percentage points. The analysis indicates that 54 clusters are required to detect a 5-percentage-point effect at 80 per cent power under this variance structure. The contribution is a formulation that makes delay equity an explicit constraint rather than an emergent property, together with a transparent account of the design burden that any credible evaluation of such a policy would carry.