Browsing by Subject "Spatial Weight Matrix"

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    Development and Application of the Network Weight Matrix to Predict Traffic Flow for Congested and Uncongested Conditions
    (2016-08-01) Ermagun, Alireza; Levinson, David M
    To capture a more realistic spatial dependence between traffic links, we introduce two distinct network weight matrices to replace spatial weight matrices used in traffic forecasting methods. The first stands on the notion of betweenness centrality and link vulnerability in traffic networks. To derive this matrix, we assume all traffic flow is assigned to the shortest path, and thereby we used Dijkstra's algorithm to find the shortest path. The other relies on flow rate change in traffic links. For forming this matrix, we employed user equilibrium assignment and the method of successive averages (MSA) algorithm to solve the network. The components of the network weight matrices are a function not simply of adjacency, but of network topology, network structure, and demand configuration. We tested and compared the network weight matrices in different traffic conditions using Nguyen-Dupuis network. The results led to a clear and unshakable conclusion that spatial weight matrices are unable to capture the realistic spatial dependence between traffic links in a network. Not only do they overlook the competitive nature of traffic links, but they also ignore the role of network topology and demand configuration. In contrast, the flow-weighted betweenness method significantly operates better than unweighted betweenness to measure realistic spatial dependence between traffic links, particularly in congested traffic conditions. The results disclosed that this superiority is more than 2 times in congested flow situations. However, forming this matrix requires considerable computational effort and information. If the network is uncongested the network weight matrix stemming from betweenness centrality is sufficient.
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    An Introduction to the Network Weight Matrix
    (2016-08-01) Ermagun, Alireza
    This study introduces the network weight matrix as a replacement for the spatial weight matrix to measure the spatial dependence between links of a network. This matrix stems from the concept of betweenness centrality and vulnerability in network science. The elements of the matrix are a function not simply of proximity, but of network topology, network structure, and demand configuration. The network weight matrix has distinctive characteristic, which are capable of reflecting spatial dependence between traffic links: (1) The elements are allowed to have negative and positive values, which capture competitive and complementary nature of links, (2) The diagonal elements are not fixed to zero, which takes the self-dependence of a link upon itself into consideration, and (3) The elements not only reflect the spatial dependence based on the network structure, but they acknowledge the demand configuration as well. We verified the network weight matrix by modeling traffic flows in a 3x3 grid test network with 9 nodes and 24 directed links connecting 72 origin-destination (OD) pairs. The results disclose models encompassing the network weight matrix outperform both models without spatial components and models with the spatial weight matrix. This leads inexorably to the conclusion that the network weight matrix represents a more accurate and defensible spatial dependency between traffic links, and thereby augments traffic flow prediction.