Static vs accumulating priorities in healthcare queues under heavy loads

TL;DR

This paper compares static and accumulating priority queueing disciplines in healthcare systems under heavy loads, showing static priorities better ensure timely care for high-priority patients during overloads.

Contribution

It provides a theoretical analysis of how static and accumulating priorities perform in overloaded healthcare queue models, highlighting the advantages of static priorities in such regimes.

Findings

Accumulating priorities lead to long waits for all patients in overload.

Static priorities ensure timely service for high-priority patients even under heavy loads.

High-priority patients are better served with static priority discipline during overloads.

Abstract

Amid unprecedented times caused by COVID-19, healthcare systems all over the world are strained to the limits of, or even beyond, capacity. A similar event is experienced by some healthcare systems regularly, due to for instance seasonal spikes in the number of patients. We model this as a queueing system in heavy traffic (where the arrival rate is approaching the service rate from below) or in overload (where the arrival rate exceeds the service rate). In both cases we assume that customers (patients) may have different priorities and we consider two popular service disciplines: static priorities and accumulating priorities. It has been shown that the latter allows for patients of 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 heavy traffic or overload regime, then all patients, including those with the highest priority, will experience very long waiting times. If on the other hand static priorities are applied, then one can ensure that the highest-priority patients will be seen in a timely manner even in overloaded systems.