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.

中文翻译：

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重载下医疗队列中的静态与累积优先级

在 COVID-19 造成的前所未有的时代，世界各地的医疗保健系统都已达到极限，甚至超出了能力极限。由于例如患者数量的季节性高峰，一些医疗保健系统经常发生类似的事件。我们将其建模为交通繁忙（到达率从下方接近服务率）或过载（到达率超过服务率）的排队系统。在这两种情况下，我们假设客户（患者）可能有不同的优先级，我们考虑两种流行的服务规则：静态优先级和累积优先级。事实证明，只要系统稳定，后者就可以及时看到所有级别的患者。然而，我们证明，如果在交通繁忙或超载情况下使用累积优先级，那么所有患者，包括具有最高优先级的患者，都将经历很长的等待时间。另一方面，如果应用静态优先级，那么即使在过载的系统中，也可以确保及时看到最高优先级的患者。