Abstract: Delay announcements have become an essential tool in service system operations: They influence customer behavior and network efficiency. We develop prediction methods for patient wait time in complex healthcare systems, where service takes a fork-join (FJ) structure. Such systems usually suffer from long delays as a result of both resource scarcity and process synchronization, even when queues are fairly short. The prediction method combines queueing-based theory methods and machine learning methods. Using data from an emergency department, we examine the accuracy and the robustness of the proposed approach, explore different model structures, and draw insights regarding the conditions under which the queuing network structure should be explicitly modeled. We provide evidence that the proposed methodology is better than other commonly used queueing theory estimators such as last-to-enter-service (which is based on snapshot-principle arguments) and queue length, and we replicate previous results showing that the most accurate estimations are obtained when using queueing model result as a feature in state-of-the-art machine learning estimation methods. We implement the prediction method in a real-time delay announcement system of an ED, showing that providing delay information to patients improves patient satisfaction and reduces the phenomena of left without being seen.