In this article, we consider joint optimization of user association and resource allocation in three tier HetNets. We formulate the objective of minimizing the resources required to clear a given set of files, as a linear program. We show that the optimal user association is determined by a rate-biasing rule, where a bias value is associated with each BS. We show that each rate-bias value crucially only takes values from a finite set which we characterize. We present a complete analytical solution along with new structural results. Using these results, we present efficient distributed algorithms for optimal control of three tier HetNets. The method involves a 1D search for a resource variable at the macro-level, and 2D search at the pico-level for a resource variable and a bias value. We apply our results to a variety of hierarchical network examples.

中文翻译：

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三层异构网络的分布式用户关联和资源分配算法

在本文中，我们考虑了三层 HetNet 中用户关联和资源分配的联合优化。我们将清除给定文件集所需的资源最小化的目标制定为线性程序。我们表明最佳用户关联是由速率偏置规则确定的，其中偏置值与每个 BS 相关联。我们表明，每个速率偏差值关键仅从我们表征的有限集合中获取值。我们提出了一个完整的分析解决方案以及新的结构结果。使用这些结果，我们提出了用于优化控制三层 HetNet 的高效分布式算法。该方法涉及在宏观级别对资源变量的一维搜索，以及在微微级别对资源变量和偏差值的二维搜索。