Traffic flow stabilized by matching speed on network with a bottleneck

We study the urban-scale traffic flow on city networks when there is a bottleneck on a road. Directed cycle graphs with and without bypasses are considered for the city traffic network. The dynamic equations of vehicular densities on all roads are presented on the networks. When vehicles flow into the connected road, the drivers are matched their speed to that at the connected road. The outflow is given by a function depending on both densities at the road and the downstream. While the outflow depends only on the density at the road in the conventional traffic model, The traffic flow is stabilized by matching the speed at the downstream. When there is a bottleneck on a road, the congestion at the bottleneck propagates over the network. The urban-scale macroscopic fundamental diagrams are derived on the graphs numerically. When there is a bottleneck on the cycle graph with and without bypasses, the fundamental diagrams are reproduced successfully. (C) 2019 Elsevier B.V. All rights reserved.