Exploring spatial characteristics of urban transportation networks

It has been shown recently that a Macroscopic Fundamental Diagram (MFD) exists in urban transportation networks under certain conditions. However, MFD is not universally expected. Previous research demonstrates the existence of MFDs in homogeneous networks with similar link densities. More recent work focuses on the partitioning of a heterogeneous transportation network based on different congestion levels. A desired partitioning produces homogeneous regions with similar link densities to guarantee a well-defined MFD and spatially compact shapes to ease the implementation of control measurements [1]. Based on recently proposed partitioning mechanism, this paper further explores the spatial characteristics of sub-networks (sub-regions or clusters) in urban transportation networks. In this paper, a metric is defined to evaluate the spatial compactness of each cluster in the network. In order to obtain the metric, a fast graph traversal algorithm is proposed, which can produce a clockwise sequence for the spatially coordinated boundary nodes along a network. The algorithm takes O(n) and the effectiveness is proved and validated. By applying the boundary smoothness metric to our previous clustering results, we show that the spatial compactness is appropriately guaranteed for each region and the future control policies can therefore be easily implemented based on the partitioning and MFDs. The proposed algorithms can have more general applications in fields of network and graph theory.