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

Recently published:

Ermagun, Alireza, and Levinson, D. (2019) Development and Application of the Network Weight Matrix to Predict Traffic Flow for Congested and Uncongested Conditions.

*Environment and Planning B: Urban Analytics and City Science*. 46(9) 1684–1705.

To capture network dependence between traffic links, we introduce two distinct network weight matrices

Wj,i, which 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 use an unweighted betweenness method and assume all traffic flow is assigned to the shortest path. The other relies on flow rate change in traffic links. For forming this matrix, we use the flow information of traffic links and employ user equilibrium assignment and the method of successive averages 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 test and compare the network weight matrices in different traffic conditions using the Nguyen–Dupuis network. The results lead to a conclusion that the network weight matrices operate better than traditional spatial weight matrices. Comparing the unweighted and flow-weighted network weight matrices, we also reveal that the assigned flow network weight matrices perform two times better than a betweenness network weight matrix, particularly in congested traffic conditions.

Figure 2. A schematic example for complementary and competitive nature of traffic links.