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

J. Selen, I.J.B.F. Adan, Vidyadhar Kulkarni, J.S.H. van Leeuwaarden

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
88 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)366-391
Number of pages26
JournalStochastic Models
Issue number3
Publication statusPublished - 2016


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