Server behaviours in healthcare queueing systems

Abstract

In the classical queueing theory literature, a server is commonly assumed to work at a constant speed. Motivated by observations from healthcare applications, a study is made to explore the nature of the relationship between service times and workload in order to assess and quantify any workforce (server) behaviours. Consequently, an initial analytical queueing model is considered with switching thresholds to allow for two-speed service. In this model service time depends on queue length, which for example captures the congestion in the waiting room and the resulting change in speed of the workforce to try and cope with the backlog of patients. Furthermore, related behavioural characteristics resulting from workload fatigue and service breakdown are considered. A developed analytical model with ‘catastrophic’ service failure is proposed to examine the consequences on patient service levels. The research helps to demonstrate the importance of more accurately capturing server behaviours in workload-dependent environments.