Queueing Models for Healthcare Operations

Patients seeking healthcare often need to wait before they can receive needed services. Excessive waiting can cause prolonged discomfort, economic loss, and long-run health complications. This motivates us to look closely at the theory of queues in order to understand the reasons why queues form and the principles underlying good system design. Queueing models help explain the interaction between resource utilization and variability. Higher resource utilization lowers the per-patient cost of making resources available, but in the presence of variability in either the service requirements or the number of service requests or both, higher utilization increases patient waiting times. In fact, for a fixed level of variability, the effect of resource utilization is highly nonlinear—waiting times increase at an increasing rate in utilization. This implies that in healthcare settings where significant variability is naturally present and difficult to eliminate, capacity planning must trade-off the cost of providing resources and the cost of patient waiting. In this chapter, we review basic queueing models that help quantify the above-mentioned tradeoff and discuss the usefulness of such models to healthcare operations managers. Specifically, we summarize some known results for queueing systems with single and multiple servers, limited and unlimited waiting room, service priority, and networks of service stations.