Synchronized flow and wide moving jams from balanced vehicular traffic

Abstract

Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental diagram of traffic flow. In the current work we analyze the steady state solutions of the new model and their stability properties. In addition to the equilibrium flow curve the trivial steady state solutions form two additional branches in the flow-density diagram. We show that the characteristic structure excludes parts of these branches resulting in the reverse $\lambda$ shape of the flow-density relation. The upper branch is metastable against the formation of synchronized flow for intermediate densities and unstable for high densities, whereas the lower branch is unstable for intermediate densities and metastable for high densities. Moreover, the model can reproduce the typical speed of the downstream front of wide moving jams. It further reproduces a constant outflow from wide moving jams, which is far below the maximum free flow. Applying the model to simulate traffic flow at a bottleneck we observe a general pattern with wide moving jams traveling through the bottleneck.

10 pages, 12 figures

References in corpus (3)

• Traffic and Related Self-Driven Many-Particle Systems
• Macroscopic Simulation of Widely Scattered Synchronized Traffic States
• Steady state solutions of hydrodynamic traffic models

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• Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts
• Theoretical vs. Empirical Classification and Prediction of Congested Traffic States
• On the Controversy around Daganzo's Requiem for and Aw-Rascle's Resurrection of Second-Order Traffic Flow Models
• Physics of Automated-Driving Vehicular Traffic
• Effect of Autonomous Driving on Traffic Breakdown in Mixed Traffic Flow: A Critical Mini-Review
• Generalizing second order macroscopic models via relative velocity of disturbances propagation in traffic flow