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Estimation of geometric route distance from its topological distance: application to narrow road networks in Tokyo
Journal of Geographical Systems ( IF 2.417 ) Pub Date : 2018-09-10 , DOI: 10.1007/s10109-018-0276-3 Hiroyuki Usui
Journal of Geographical Systems ( IF 2.417 ) Pub Date : 2018-09-10 , DOI: 10.1007/s10109-018-0276-3 Hiroyuki Usui
The structure of road networks has been investigated in accordance with the development of GIScience. By classifying road networks into wide and narrow ones, we can define the route as the path from the route’s origin (also called the root) on a wide road network to a narrow road segment which consists of the sequence of narrow road segments arranged by ascending order of the number of steps of adjacency to its root. The length of the route can be defined with the following geometric and topological terms: the route distance, measuring the length along the route and the depth, counting the number of road segments on the route. The depth plays the important role of being a substitute for the route distance in modelling road networks as a planar graph. Since road networks clearly exhibit irregular patterns and road segment lengths are non-uniform, it is considered appropriate to adopt a stochastic approach rather than a deterministic one to analyse the route distance. However, the relationship between the route distance and its depth has not been sufficiently investigated stochastically. Therefore, the research question is how can we estimate the route distance from its depth? Based on an empirical study in the Tokyo metropolitan region, it was found that (1) the statistical distribution of the route distance can be formulated as an Erlang distribution whose parameters are its depth and the inverse of the mean length of narrow road segments, and (2) this length is constant and close to 40 m. Therefore, we can estimate the route distance from only one parameter, the depth. Also, as a practical application, accessibility to the kth depth link in terms of firefighting was evaluated because the maximum length of the extension of fire hoses is approximately 200 m. It was found that (1) even if k ≤ 5, the probability that the route distance to the kth depth link is equal to or longer than 200 m ranges from 0 to 0.45; and (2) if k ≥ 8, the probability is approximately 1. These indicate the limitation of the deterministic approach because, on the basis of complete grid patterns (with intervals of 40 m between intersections), k = 5 corresponds to a distance of 200 m from wide road networks and the route to the 5th depth link can be covered with fire hoses. Moreover, it was found that the connectivity of wide road networks is higher than that of narrow ones in terms of the smaller ratio of cul-de-sacs and the larger ratio of four-way intersections. These answers contribute substantially not only to constructing a science of cities that provides a simple model and specifies the most important parameter, but also to our understanding of the structure of narrow road networks within several hundred metres of wide road networks.
中文翻译:
从拓扑距离估计几何路径距离:在东京的狭窄道路网络中的应用
随着GIS科学的发展,对道路网络的结构进行了研究。通过将道路网络分为宽阔和狭窄的网络,我们可以将路线定义为从宽阔的道路网络上的路线的起点(也称为根)到狭窄的路段的路径,该路段由按升序排列的一系列狭窄路段组成与其根相邻的步骤数的顺序。路线的长度可以用以下几何和拓扑术语定义:路线距离,沿路线的长度和深度的测量,计算路线上的路段数。在将道路网络建模为平面图时,深度起着替代路线距离的重要作用。由于道路网络明显显示出不规则的模式,并且路段长度不均匀,因此采用随机方法而不是确定性方法来分析路线距离被认为是适当的。但是,尚未对随机距离充分研究路径距离及其深度之间的关系。因此,研究的问题是如何从深度出发估算路径距离?根据对东京都会区的一项实证研究,发现(1)路线距离的统计分布可以公式化为Erlang分布,其参数为深度和窄路段平均长度的倒数,以及(2)该长度是恒定的,接近40 m。因此,我们可以仅根据一个参数(深度)估算路线距离。另外,在实际应用中,由于消防水龙带的最大延伸长度约为200 m,因此评估了在消防方面通往第k个深层连接的可及性。结果发现,(1)即使ķ ≤5中,所涉及的路径距离的概率ķ个深度链路等于或长于从0至0.45200米范围; 和(2)如果ķ ≥8,概率大约为1。这些指示确定性方法的限制,因为,完全网格图案的基础上(带的相交处之间40米间隔)ķ = 5个对应于200米宽的道路的距离网络和通往第5个深度链接的路线可以用消防水带覆盖。此外,还发现,由于死胡同的比例较小,而四通交叉口的比例较大,因此宽阔的道路网络的连通性高于狭窄的道路网络。这些答案不仅有助于构建提供简单模型并指定最重要参数的城市科学,而且有助于我们理解数百米宽路网中的窄路网的结构。
更新日期:2018-09-10
中文翻译:
从拓扑距离估计几何路径距离:在东京的狭窄道路网络中的应用
随着GIS科学的发展,对道路网络的结构进行了研究。通过将道路网络分为宽阔和狭窄的网络,我们可以将路线定义为从宽阔的道路网络上的路线的起点(也称为根)到狭窄的路段的路径,该路段由按升序排列的一系列狭窄路段组成与其根相邻的步骤数的顺序。路线的长度可以用以下几何和拓扑术语定义:路线距离,沿路线的长度和深度的测量,计算路线上的路段数。在将道路网络建模为平面图时,深度起着替代路线距离的重要作用。由于道路网络明显显示出不规则的模式,并且路段长度不均匀,因此采用随机方法而不是确定性方法来分析路线距离被认为是适当的。但是,尚未对随机距离充分研究路径距离及其深度之间的关系。因此,研究的问题是如何从深度出发估算路径距离?根据对东京都会区的一项实证研究,发现(1)路线距离的统计分布可以公式化为Erlang分布,其参数为深度和窄路段平均长度的倒数,以及(2)该长度是恒定的,接近40 m。因此,我们可以仅根据一个参数(深度)估算路线距离。另外,在实际应用中,由于消防水龙带的最大延伸长度约为200 m,因此评估了在消防方面通往第k个深层连接的可及性。结果发现,(1)即使ķ ≤5中,所涉及的路径距离的概率ķ个深度链路等于或长于从0至0.45200米范围; 和(2)如果ķ ≥8,概率大约为1。这些指示确定性方法的限制,因为,完全网格图案的基础上(带的相交处之间40米间隔)ķ = 5个对应于200米宽的道路的距离网络和通往第5个深度链接的路线可以用消防水带覆盖。此外,还发现,由于死胡同的比例较小,而四通交叉口的比例较大,因此宽阔的道路网络的连通性高于狭窄的道路网络。这些答案不仅有助于构建提供简单模型并指定最重要参数的城市科学,而且有助于我们理解数百米宽路网中的窄路网的结构。