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

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

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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
Number of pages27
Publication statusPublished - 2015

Publication series

Volume1502.02856 [math.PR]


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