A Simulation Analysis on the Existence of Network Traffic Flow Equilibria

A macroscopic fundamental diagram (MFD) can be applied to design simple and effective traffic network control strategies to prevent congestion in an urban traffic network. Network flow equilibria on MFDs are important properties for designing effective network controllers for urban traffic networks. In order to verify the existence of equilibria on MFDs, microscopic simulations are run for an urban traffic network with various network input traffic flows and traffic-signal control strategies. The simulation results show that the traffic network can reach its network flow equilibria if the traffic flows in the network are in the linear region (the free-flow region) of the MFD, although the network flows are heterogeneous; however, network flow equilibria do not exist for the nonlinear region (the non-free-flow region) of the MFD unless the traffic network flows are homogeneous. Properly designed traffic-signal control strategies can improve the degree of traffic flow homogeneity; thus, network flow equilibria are easy to be achieved under a bounded network input flow.