We study the occurrence of large queue lengths in the GI / GI / d queue with heavy-tailed Weibull-type service times. Our analysis hinges on a recently developed sample path large-deviations principle for Lévy processes and random walks, following a continuous mapping approach. Also, we identify and solve a key variational problem which provides physical insight into the way a large queue length occurs. In contrast to the regularly varying case, we observe several subtle features such as a non-trivial trade-off between the number of big jobs and their sizes and a surprising asymmetric structure in asymptotic job sizes leading to congestion.

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Queueing Systems
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Bazhba, M., Blanchet, J., Rhee, C.-H., & Zwart, B. (2019). Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times. Queueing Systems, 93(3-4), 195–226. doi:10.1007/s11134-019-09640-z