The snowball effect of customer slowdown in critical many-server systems. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Selen, Jori; Adan, Ivo J. B. F.; Kulkarni, Vidyadhar G.; van Leeuwaarden, Johan S. H.
• Is Part Of: Stochastic models. Volume 32:Issue 3(2016)
• Page Start: 366
• Page End: 391
• Publication Date: 2016-07-02
• Subjects: Bistability; quasi-birth-and-death process; QED scaling; queueing theory; slowdown; 60J27; 60K25; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2015.1136221
• Languages: English
• ISSNs: 1532-6349

Abstract

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.