Numerical simulation of Car-Following Model Considering Multiple-Velocity Difference and Changes with Memory

Abstract

In order to enhance the stability of car-following traffic flow in the traffic system, based on the full velocity difference (FVD) model, a Multiple-Velocity Difference and Changes with Memory (MVDCM) model is deduced with comprehensive consideration of the velocity difference and memory effect of multiple preceding vehicles. In the model, we introduce the velocity difference information and changes with memory effect of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> vehicles in front, in order to solve the delay problem in the FVD model caused by the indirect analysis of the velocity information of the front and rear vehicles. By using linear stability analysis and figure out the critical conditions for judging the stability of the traffic flow, then use Matlab to do numerical simulations and analyses. Simulation results show that under the same initial disturbance conditions, the MVDCM model has a lower velocity fluctuation and a larger stable area than the optimal velocity (OV) model, the FVD model and the Multiple-Velocity difference (MVD) model, especially when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k=3,\ \lambda=0.2$</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\gamma=0.1$</tex> , the average volatility is as low as 0.26%. Consequently, the proposed model can effectively improve the stability of the car-following traffic system and alleviate traffic jams.