Continuous-Time Monitoring of Queueing Processes

In recent years, effective monitoring of categorical and count data has increasingly attracted attention of researchers in thearea of statistical process control. However, most of the existing research model categorical and count data streams as independentand identically distributed data or serially correlated discrete time stochastic processes. Very limited research has been conducted formonitoring continuous-time stochastic processes (CTSPs). This paper develops a novel statistical monitoring method for CTSPs with afocus on queueing processes. The proposed method is based on detecting a change in the intensity function of such processes, usingan approximate likelihood ratio test. The approximation method is both computationally easy for real-time implementation andwell-suited for the introduction of penalization methods. Simulation results based on Markovian and non-Markovian queues show thatthe proposed methods effectively detect temporal changes in the queueing process. A case study focusing on monitoring the bedassignment process of patients visiting an emergency department demonstrates the efficacy of the proposed methods in a healthcaresystem