Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete-time stochastic models for which we derive heavy-traffic approximations that are scalable in the system size. Subsequently, we show how this leads to novel capacity sizing rules that acknowledge the presence of overdispersion. This, in turn, leads to robust approximations for performance characteristics of systems that are of moderate size and/or may not operate in heavy traffic.

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Queueing Systems
Rare events: Asymptotics, Algorithms, Applications
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Mathijsen, B., Janssen, A. J. E. M., van Leeuwaarden, J., & Zwart, B. (2018). Robust heavy-traffic approximations for service systems facing overdispersed demand. Queueing Systems, 90, 257–289. doi:10.1007/s11134-018-9584-z