Online Learning and Optimization for Queues with Unknown Arrival Rate and Service Distribution

End-to-End Optimization for Queues Beyond PTO Most queueing optimization methods rely on a predict-then-optimize (PTO) paradigm, which first estimates key model primitives (e.g., demand rates and service-time distributions) and then optimizes system decisions using these estimates as if they were exact. In practice, however, queueing performance formulas are often highly sensitive to estimation errors, especially under congestion, making such approaches fragile and potentially misleading. In “Online Learning and Optimization for Queues with Unknown Arrival Rate and Service Distribution,” X. Chen, G. Hong, and Y. Liu develop a new end-to-end online learning framework for jointly optimizing pricing and capacity decisions in service systems, called LiQUAR (learning in queue with unknown arrival rate). LiQUAR is specialized to queueing systems by explicitly leveraging workload dynamics and transient behavior, allowing it to learn directly from arrival and service data without requiring prior knowledge of the demand function or the service-time distribution. Designing online learning algorithms for queues poses unique challenges: Data are temporally correlated, system dynamics are disrupted by policy updates, and performance is highly sensitive to congestion. LiQUAR addresses these challenges through queue-aware algorithm design and analysis, establishing regret bounds that capture the effect of traffic intensity and demonstrating superior performance to PTO and gradient-based reinforcement learning methods, particularly in heavily loaded systems.