Design airport dispatch with ETA uncertainty

You control airport pickups with streaming ETAs for arriving flights and live driver locations/queues. Design an online dispatch algorithm that minimizes passenger wait time and deadhead miles under constraints: vehicle capacity, maximum pickup window, staging lot limits, and driver time-on-app. Assume ETA uncertainty is approximately normal with σ ≈ 5 minutes and ETAs update every minute; drivers have heterogeneous distances and service times. Specify the objective function, data structures, and algorithmic approach (e.g., min-cost flow with recourse, online bipartite matching with predicted costs) and how you handle ETA updates, cancellations, and fairness. Analyze complexity, discuss competitive ratio or worst-case bounds, and propose a fallback strategy during demand spikes.