Likelihood ratio-based CUSUM charts for real-time monitoring the quality of service in a network of queues

Queuing networks (QNs) are widely used stochastic models for service systems include healthcare systems, transportation systems, and computer networks. While existing literature has extensively focused on modeling and optimizing resource allocation in QNs, very little research has been done on developing systematic statistical monitoring methods for QNs. This paper proposes cumulative sum (CUSUM) control charts that monitor the queuing information collected in real-time from the QN. We compare the proposed methods with existing statistical monitoring methods to demonstrate their ability to quickly detect a change in the service rate of one or more queues at the nodes in the QN. Simulation results show that the proposed CUSUM charts are more effective than existing statistical monitoring methods. The motivation for this research comes from the need to monitor the performance of a hospital emergency department (ED) with the goal of monitoring delays experienced by patients visiting the ED. A case study using the data from the ED of a large academic medical center shows that proposed methods are a promising tool for monitoring the timeliness of care provided to patients visiting the ED.