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(If audience are graduate students or senior undergrad.)
1. Conservation of mass equation.
Convert Eulerian to Lagrangian coordinate.
Viscous shocks, and rarefaction waves, Lax entropy condition.
Solutions to Riemann problems.
2. LWR model for traffic. deceleration shocks and acceleration rarefaction waves.
Wave interactions.
LWR model dissipates speed oscillations and hence it does not generate traffic jams.
Numerical solutions of LWR model.
3 . Real traffic jams data.
Sugiyama experiment.
Agreement and disagreements between LWR and real traffic.
Past effort of fixing LWR: other macroscopic models.
Still cannot produce stop-and-go waves.
4. Hysteresis, what is it?
Including hysteresis into LWR.
New model = LWR+hysteresis
Waves of the model for traffic involving hysteresis.
Stop-and-go solutions. This is what past models cannot do.
5. Example solutions simulating real traffic phenomena.
Numerical scheme for the model.
The model's wave tracking analysis and numerical simulation resembles Sugiyama experiment.
A mechanism for traffic jam formation, and simulation.
6. Dissipating traffic jams using controlled autonomous cars