Ripley’s K-function for Network-Constrained Flow Data

Abstract

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.