# Development and Application of the Network Weight Matrix to Predict Traffic Flow for Congested and Uncongested Conditions

Recent working paper

Ermagun, Alireza, and Levinson, D. (2016) Development and Application of the Network Weight Matrix to Predict Traffic Flow for Congested and Uncongested Conditions (

*Working Paper*).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.