Inequalities in the Theory of Queues
Inequalities in the Theory of Queues
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队列理论中的不等式
DOI：
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
J. Kingman
中科院分区：
文献类型：
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作者：
J. Kingman
它是一个公平的批评理论的排队，因为它已经发展多年来，即使在简单的情况下，明确的分析解决方案可以找到，这些解决方案往往过于复杂，是实际使用。有人在其他地方（金曼，1966年）提出，在某种程度上，通过分析存在鲁棒近似的情况，如“交通繁忙”的情况，可以满足这种批评。然而，重要的是要知道这些近似值如何准确地代表真正的解，因此，各种感兴趣的量的不等式的重要性变得显而易见。为了有用，不等式必须具有两个在某种程度上彼此不相容的性质。如果0是一个可能不容易计算的量，那么不等式0 < 6'就不会有意义，除非有理由希望，在适当的意义上，6'合理地接近于0。当然，如果不等式是一对不等式中的一个，则最好确定这一点
IT is a fair criticism of the theory of queues as it has developed through the years that, even in the simple cases for which explicit analytical solutions can be found, these solutions are often too complicated to be of practical use. It has been argued elsewhere (Kingman, 1966) that the criticism is to be met to some degree by the analysis of situations where robust approximations exist, such as that of "heavy traffic". It is, however, important to know how accurately such approximations represent the true solution, and the significance of inequalities for the various quantities of interest thus becomes apparent. To be useful, an inequality must have two properties which are to some extent incompatible with one another. If 0 is some quantity not perhaps easy to calculate, the inequality 0 < 6' will not be significant unless there is reason to hope that, in an appropriate sense, 6' is reasonably close to 0. This can of course best be determined if the inequality is one of a pair