Bazhba, M., Blanchet, J., Rhee, CH. et al. Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times. Queueing Syst 93, 195–226 (2019). https://doi.org/10.1007/s11134-019-09640-z
Abstract
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.
Authors
Mihail Bazhba, Jose Blanchet, Chang-Han Rhee, Bert Zwart
Publication date
2019/12
Journal
Queueing Systems
Volume
93
Pages
195-226
Publisher
Springer US
