The snowball effect of customer slowdown in critical many-server systems

TL;DR

This paper investigates the impact of customer slowdown in many-server systems, revealing how delays can cause a snowball effect that worsens system performance, especially under heavy traffic, with implications for healthcare and service operations.

Contribution

It introduces a two-dimensional Markov model for threshold slowdown in many-server systems and analyzes the detrimental effects and bistable behavior caused by customer delays.

Findings

Slowdown leads to longer customer service times and delays.

Heavy-traffic conditions exacerbate the snowball effect.

Neglecting slowdown causes significant underprovisioning issues.

Abstract

Customer slowdown describes the phenomenon that a customer's service requirement increases with experienced delay. In healthcare settings, there is substantial empirical evidence for slowdown, particularly when a patient's delay exceeds a certain threshold. For such threshold slowdown situations, we design and analyze a many-server system that leads to a two-dimensional Markov process. Analysis of this system leads to insights into the potentially detrimental effects of slowdown, especially in heavy-traffic conditions. We quantify the consequences of underprovisioning due to neglecting slowdown, demonstrate the presence of a subtle bistable system behavior, and discuss in detail the snowball effect: A delayed customer has an increased service requirement, causing longer delays for other customers, who in turn due to slowdown might require longer service times.