Dynamic User Equilibrium in the Morning Peak Period

This paper formulates a dynamic user equilibria model that incorporates the traffic congestion based on the flow-density fundamental diagram. By using Greenshieldpsilas speed-density relationship, we derive the analytical solution, which is different with not only the traditional static BPR function but also the classical bottleneck model result. In the free regime, the equilibrium cost is a power function of the total demand, which is more similar to the BPR function. While in the congested regime, the equilibrium cost is a monotonic increasing linear function of the total demand and larger than bottleneck model equilibrium cost.