Large language models are increasingly used in decision-support systems where uncertain or high-risk queries can be referred to human experts, but expert capacity is limited and deferral decisions must account for both model reliability and congestion in the expert-review queue. This project will develop and evaluate queue-aware online learning methods that decide, for each incoming query, whether to accept an LLM response or defer it to a capacity-constrained expert while learning the reliability of the LLM’s confidence signal from selectively observed and delayed expert feedback. The project will investigate scalable algorithms that jointly balance prediction error, information acquisition, and expert-queue congestion, and will evaluate them through large-scale LLM inference and stochastic simulation across multiple models, reasoning and question-answering datasets, uncertainty mechanisms, and expert-service regimes. The goal is to establish robust and computationally efficient principles for human–AI collaboration in settings where limited expert attention must be allocated dynamically while maintaining reliable automated decision making.