On the spatial partitioning of urban transportation networks

It has been recently shown that a macroscopic fundamental diagram (MFD) linking space-mean network flow, density and speed exists in the urban transportation networks under some conditions. An MFD is further well defined if the network is homogeneous with links of similar properties. This collective behavior concept can also be utilized to introduce simple control strategies to improve mobility in homogeneous city centers without the need for details in individual links. However many real urban transportation networks are heterogeneous with different levels of congestion. In order to study the existence of MFD and the feasibility of simple control strategies to improve network performance in heterogeneously congested networks, this paper focuses on the clustering of transportation networks based on the spatial features of congestion during a specific time period. Insights are provided on how to extend this framework in the dynamic case. The objectives of partitioning are to obtain (i) small variance of link densities within a cluster which increases the network flow for the same average density and (ii) spatial compactness of each cluster which makes feasible the application of perimeter control strategies. Therefore, a partitioning mechanism which consists of three consecutive algorithms, is designed to minimize the variance of link densities while maintaining the spatial compactness of the clusters. Firstly, an over segmenting of the network is provided by a sophisticated algorithm (Normalized Cut). Secondly, a merging algorithm is developed based on initial segmenting and a rough partitioning of the network is obtained. Finally, a boundary adjustment algorithm is designed to further improve the quality of partitioning by decreasing the variance of link densities while keeping the spatial compactness of the clusters. In addition, both density variance and shape smoothness metrics are introduced to identify the desired number of clusters and evaluate the partitioning results. These results show that both the objectives of small variance and spatial compactness can be achieved with this partitioning mechanism. A simulation in a real urban transportation network further demonstrates the superiority of the proposed method in effectiveness and robustness compared with other clustering algorithms. (C) 2012 Elsevier Ltd. All rights reserved

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