The Battle of Infinity: Explosive Demand Surge vs Gigantic Service Providers

TL;DR

This paper introduces a stability criterion for infinite server queues to handle heavy-tailed demand surges, with applications to healthcare systems during pandemics, highlighting when such systems can become overwhelmed.

Contribution

It develops a new stability criterion based on the Borel-Cantelli lemma for infinite server queues under heavy-tailed demands, illustrating conditions leading to overload.

Findings

Heavy-tailed demand can overwhelm infinite servers.

Healthcare systems must consider tail behavior during pandemics.

The criterion helps assess system stability under explosive demand.

Abstract

Infinite server queues have ultimate processing power to accommodate explosive demand surges. We provide a new stability criterion based on the Borel-Cantelli lemma to judge whether the infinite server safely accommodates heavy-tailed demands. We illustrate the battles between heavy-tailed demand and infinite servers in detail. In particular, we show some cases where the explosive demand overwhelms the infinite server queue. The medical demand caused by pandemics such as the COVID- 19 creates huge stress to the healthcare system. This framework indicates that healthcare systems need to account for the tail behavior of the cluster size and hospital stay length distributions to check the stability of their systems during pandemics.