The snowball effect of customer slowdown in critical many-server systems |
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Authors: | Jori Selen Ivo J. B. F. Adan Vidyadhar G. Kulkarni Johan S. H. van Leeuwaarden |
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Affiliation: | 1. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands;2. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands;3. Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, North Carolina, USA;4. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands |
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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. |
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Keywords: | Bistability quasi-birth-and-death process QED scaling queueing theory slowdown |
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