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Our analysis hinges on a recently developed sample path large-deviations principle for L\u00e9vy 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.<\/jats:p>","DOI":"10.1007\/s11134-019-09640-z","type":"journal-article","created":{"date-parts":[[2019,11,10]],"date-time":"2019-11-10T05:02:31Z","timestamp":1573362151000},"page":"195-226","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times"],"prefix":"10.1007","volume":"93","author":[{"given":"Mihail","family":"Bazhba","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jose","family":"Blanchet","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chang-Han","family":"Rhee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9336-0096","authenticated-orcid":false,"given":"Bert","family":"Zwart","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,11,10]]},"reference":[{"key":"9640_CR1","unstructured":"Pollaczek, F\u00e9lix: Th\u00e9orie analytique des probl\u00e8mes stochastiques relatifs \u00e0 un groupe de lignes t\u00e9l\u00e9phoniques avec dispositif d\u2019attente (1961)"},{"key":"9640_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0002-9947-1955-0066587-3","volume":"78","author":"J Kiefer","year":"1955","unstructured":"Kiefer, J., Wolfowitz, J.: On the theory of queues with many servers. 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