Recently we proposed an extension to the traffic model of Aw, Rascle andGreenberg. The extended traffic model can be written as a hyperbolic system ofbalance laws and numerically reproduces the reverse $\lambda$ shape of thefundamental diagram of traffic flow. In the current work we analyze the steadystate solutions of the new model and their stability properties. In addition tothe equilibrium flow curve the trivial steady state solutions form twoadditional branches in the flow-density diagram. We show that thecharacteristic structure excludes parts of these branches resulting in thereverse $\lambda$ shape of the flow-density relation. The upper branch ismetastable against the formation of synchronized flow for intermediatedensities and unstable for high densities, whereas the lower branch is unstablefor intermediate densities and metastable for high densities. Moreover, themodel can reproduce the typical speed of the downstream front of wide movingjams. It further reproduces a constant outflow from wide moving jams, which isfar below the maximum free flow. Applying the model to simulate traffic flow ata bottleneck we observe a general pattern with wide moving jams travelingthrough the bottleneck.
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