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Amid unprecedented times caused by COVID-19, healthcare systems all over theworld are strained to the limits of, or even beyond, capacity. A similar eventis experienced by some healthcare systems regularly, due to for instanceseasonal spikes in the number of patients. We model this as a queueing systemin heavy traffic (where the arrival rate is approaching the service rate frombelow) or in overload (where the arrival rate exceeds the service rate). Inboth cases we assume that customers (patients) may have different prioritiesand we consider two popular service disciplines: static priorities andaccumulating priorities. It has been shown that the latter allows for patientsof all classes to be seen in a timely manner as long as the system is stable.We demonstrate however that if accumulating priorities are used in the heavytraffic or overload regime, then all patients, including those with the highestpriority, will experience very long waiting times. If on the other hand staticpriorities are applied, then one can ensure that the highest-priority patientswill be seen in a timely manner even in overloaded systems.

Static vs accumulating priorities in healthcare queues under heavy loads