Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in \({\mathbb {R}}^n\), with the admissible set indexed by the time parameter. The structure of the constraints depends on the underlying network topology. We investigate continuity and monotonicity of the resulting maximizers with respect to time. Our results have important consequences for fluid models of the corresponding networks which are optimal, in the appropriate sense, with respect to handling real-time transmission requests.

中文翻译：

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贪婪最大化问题解的连续性和单调性

受资源共享网络建模应用的推动，我们考虑了\（{\ mathbb {R}} ^ n \）中向量的贪婪最大化（即连续最小值的最大化）的问题，可允许集的索引为时间参数。约束的结构取决于基础网络拓扑。我们研究相对于时间的结果最大化器的连续性和单调性。我们的结果对相应网络的流体模型具有重要的影响，在适当的意义上，这些模型在处理实时传输请求方面是最佳的。