Artificial Intelligence Distributionally Robust Optimisation of Telemedicine Bandwidth Allocation Under Variable Rural Network Congestion Telemetry: A computed Healthcare Consultation Completion Equity Evaluation

Rural telemedicine consultations fail not because bandwidth is absent but because congestion telemetry is unreliable, and allocation rules tuned to average congestion systematically under-serve the clinics whose links degrade most. the present analysis formulates bandwidth allocation across a rural consultation network as a distributionally robust optimisation problem in which the ambiguity set is an f-divergence ball around the empirical congestion distribution reported by each link, and the objective is to maximise the worst-case expected number of completed consultations subject to per-clinic completion-equity constraints. The formulation is solved by a dual reformulation that reduces to a tractable convex program, and its operating characteristics are evaluated in a replication-based replication of a before-after-control-impact design with 8, 16, 24 and 32 clusters, effect sizes of 3, 5 and 8 percentage points, and 2000 replications per design cell under a declared variance structure with between-cluster SD 6.0, residual SD 4.5 and intraclass correlation 0.64. The analysis characterises how estimated power, minimum detectable effect and interval coverage behave as cluster count and effect size vary, and identifies the cluster count at which a 5 percentage point equity effect is detectable at 80% power. The contribution is a decision rule that prices telemetry ambiguity explicitly, together with a design-level account of what a rural telemedicine equity evaluation can and cannot resolve.