Stady on Analysis and Optimization of Urban Spatial Hierarchical Structure

本研究旨在建立一种描述和优化设施空间结构中层次结构的方法。首先，我们发展了一种图论方法来分析设施的空间层次。利用该方法，我们可以用几个指标来描述空间层次；树的长度，树的宽度和K值。我们将这种方法应用于西宫的商店，并将其与两种层次结构进行比较，一种来自Christaller定律，另一种来自空间随机性。我们由此得出结论，在现实世界中发现的空间层次往往似乎具有一种规律性，但这种规律性可以在空间随机性中找到。其次，我们将该方法扩展到网络空间。通过这种扩展，我们可以从行为模型的角度来分析空间结构。我们将这种方法应用于零售设施、公立学校和邮局的分析。从这个分析中，我们得到了一些重要的发现。第三，我们开发了一种计算算法来优化设施的分层结构。已经有几种算法可以优化设施的位置，但它们不能使我们优化层次结构本身。我们的算法是解决这个问题的一种方法。为了验证该方法的有效性，我们将其应用于邮件传递系统的优化，得到了一个近乎理想的结构。

This study aims to develop a method for describing and optimizing the hierarchical stucture found in the spatial structure of facilities. First, we develop a graph theoretical method to analyze a spatial hierarchy of facilities. With a help of this method, we can describe a spatial hierarchy by several indices ; tree lengh, tree width, and K value. We apply this method to the stores in Nishinomiya, and compared it with two hierarchical structures, one derived from the Christaller's law, and the other from a spatial randomness. We consequently concluded that the spatial hierarchy found in the real world often seemds to have one kind of regularity, but such regularity can be found in a spatial randomness. Second, we expand this method to a space on network. By this expansion, we can analyze the spatial structure from a view of behavioral models. We applied this method to the analysis of retail facilities, public schools, and post offices. From this analysis, we obtained some important findings. Third, we develop a computational algorithm to optimize hierarchical structures of facilities. There are already several algorithms to optimize the location of facilities, but they do not enables us to optimize the hierarchical structure itself. Out algorithm is one solution to this problem. To test the validity of this method, we applied it to the optimization of mail delivery system, and we could obtain an almost ideal structure.