Feature-Driven Priority Queuing

Traditional queuing theory assumes that job types are perfectly observed and assigns each job to a type-specific priority queue—an approach we term type-driven priority queuing. We study feature-driven priority queuing, where types are unobserved and must be inferred from observable features using a classifier. We examine two implementations. The first, type-first, predicts type probabilities from features and then maps these probabilities to priority queues. The second, direct, bypasses type prediction and maps features directly to priority queues in an end-to-end manner. The classifiers in both implementations can be trained using labeled data of features (e.g., chest X-rays) with types (e.g., disease findings), but we train the direct classifier to minimize empirical waiting cost rather than type-prediction error. In the type-first approach, the type classifier is optimized and locked in the first stage; queue assignment is then optimized to minimize an estimated waiting cost computed from the type classifier’s output distribution. The actual waiting cost, however, depends on the underlying feature distributions. The estimated waiting cost converges to the actual waiting cost only when the classifier recovers the Bayes posterior—a condition rarely satisfied by complex, misspecified models in high-dimensional settings. The direct approach instead optimizes an empirical waiting cost computed directly from the type-labeled features, ensuring convergence to the actual waiting cost and yielding systematically better queue assignments. We prove this advantage analytically, demonstrate it in tractable examples, and confirm it in large-scale simulations. In experiments with 100,000 chest X-rays and state-of-the-art deep learning classifiers, the direct approach substantially reduces average radiologist waiting cost, driven by its ability to jointly capture delay-cost differences and limited feature separability when assigning priorities.

Funding: The work of I. Gurvich was supported by the National Science Foundation [Grant DIS-1935809].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.0754.