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 Levy 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.

中文翻译：

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具有重尾 Weibull 服务时间的多服务器队列的队列长度渐近性

我们研究了具有重尾 Weibull 类型服务时间的 GI / GI / d 队列中大队列长度的发生。我们的分析取决于最近为 Levy 过程和随机游走开发的样本路径大偏差原理，遵循连续映射方法。此外，我们识别并解决了一个关键的变分问题，该问题提供了对大队列长度发生方式的物理洞察。与定期变化的情况相比，我们观察到几个微妙的特征，例如大型作业的数量与其规模之间的重要权衡，以及导致拥塞的渐近作业规模中令人惊讶的不对称结构。