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.

Heavy tails, Multiple-server queue, Queue length asymptotics, Weibull service times
Queueing Systems
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Bazhba, M, Blanchet, J, Rhee, C.H, & Zwart, A.P. (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