2020/08/31 by Hiroshi Toyoizumi, Toyoizumi, Hiroshi
Business, Management and Accounting · Economics, Econometrics and Finance · #Advanced Queuing Theory Analysis #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2008.13360
openalex publication_date 2020/08/31 · openalex created_date 2020/09/08 · openalex updated_date 2026/07/28
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.