This paper studies tight upper bounds for the mean and higher moments of the steady-state waiting time in the GI/GI/1 queue given the first two moments of the interarrival-time and service-time distributions. We apply the theory of Tchebycheff systems to obtain sufficient conditions for classical two-point distributions to yield the extreme values. These distributions are determined by having one mass at 0 or at the upper limit of support.

中文翻译：

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给定两个时刻的极值 GI/GI/1 队列：利用 Tchebycheff 系统

考虑到到达间隔时间和服务时间分布的前两个时刻，本文研究了 GI/GI/1 队列中稳态等待时间的均值和较高时刻的紧上界。我们应用 Tchebycheff 系统的理论来获得经典两点分布产生极值的充分条件。这些分布是通过在 0 或支持上限处具有一个质量来确定的。