Improved Car-Following Model for Traffic Flow and Its Numerical Simulation on Highway with Gradients

We investigated the effect of the slope upon traffic flow on a single lane highway with an uphill gradient and a downhill gradient. The model was improved by introducing the variable brake distance on different gradient. A simulation is carried out to examine the validity and reasonability of the improved model. The result of the simulation shows that the amplitude of the density waves decreases with the decrease of the slope of the gradient on highway. Moreover the density waves propagate backward. The results indicated that the new model was reasonable and valid in describing the motion of the vehicles on highway with some gradients.