LLM scheduling control planes earn their cost only under non-stationary load

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Testing deadline-aware mixed-criticality scheduling at the autonomous-vehicle edge, the authors first build a strong heuristic — a windowed contract-net auction ordering each admission window time-critical-first by earliest deadline, placing by earliest finish time — which hits a 0.902 time-critical completion rate across 60 instances and 15 baselines (best baseline 0.838, Holm-corrected p < 0.001) at 0.87 of a CP-SAT upper bound. Adding a multi-agent LLM control plane contributes nothing while load is stationary; the advantage traces to batching horizon and TC-first ordering alone. Only under a mid-run surge of safety-critical tasks does the LLM layer beat both the static heuristic and a bandit. Code and seeded instances are released.