Many types of spatial flows, including pedestrian flows and vehicle flows, are constrained by and distribute on spatial networks. In the literature, network-constrained flows are usually modeled as a direct line in planar space using methods designed for flows in planar space. Further, in spatial statistical analysis of flow patterns, distance measures and the hypothesis of spatial randomness of flows also have a significant impact on the determination of flow patterns. In this study, we extend the global and local Ripley’s K functions for planar flows to network space. Both the network and planar K-functions for flows are applied to detect the patterns of taxi Origin-Destination flow data on a road network at multiple scales. The effect of distance measures and simulation methods in the network and planar Ripley’s K functions are examined. We found that the planar K function is more sensitive to the changes in scale and tends to detect more clustered flows compared with the network K function at the same scale. Distance measures and simulation methods have a more significant influence on the detection of patterns of network-constrained flows than the selection of the network or planar Ripley’s K functions. This study suggests that distance measures and hypotheses of spatial randomness have to be chosen carefully before applying flow pattern analytic methods to network-constrained flows and interpreting the results of flow patterns.

中文翻译：

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网络约束流数据的 Ripley 函数

许多类型的空间流，包括行人流和车辆流，都受到空间网络的约束和分布。在文献中，网络约束流通常使用为平面空间中的流设计的方法建模为平面空间中的直线。此外，在流型的空间统计分析中，距离度量和流的空间随机性假设也对流型的确定产生重大影响。在这项研究中，我们将平面流的全局和局部 Ripley's K 函数扩展到网络空间。流的网络和平面 K 函数都应用于检测多尺度道路网络上出租车起点-目的地流数据的模式。检查距离测量和模拟方法在网络和平面 Ripley 的 K 函数中的效果。我们发现，与相同尺度下的网络 K 函数相比，平面 K 函数对尺度变化更敏感，并且倾向于检测到更多的聚集流。距离测量和模拟方法对网络约束流模式的检测比网络或平面 Ripley's K 函数的选择具有更显着的影响。这项研究表明，在将流动模式分析方法应用于网络受限的流动和解释流动模式的结果之前，必须仔细选择距离测量和空间随机性假设。距离测量和模拟方法对网络约束流模式的检测比网络或平面 Ripley's K 函数的选择具有更显着的影响。这项研究表明，在将流动模式分析方法应用于网络受限的流动和解释流动模式的结果之前，必须仔细选择距离测量和空间随机性假设。距离测量和模拟方法对网络约束流模式的检测比网络或平面 Ripley's K 函数的选择具有更显着的影响。这项研究表明，在将流动模式分析方法应用于网络受限的流动和解释流动模式的结果之前，必须仔细选择距离测量和空间随机性假设。