Institute of Transportation, MOTC

　　Microscopic car-following models can accurately describe individual driving behaviors within traffic flows. However, due to their complicated model formulation, only linear car-following models have been established for stability analysis, and non-linear models have always been a lackluster. This paper aimed to analyze the stability of car-following models by simulation. Simulation results showed that under the condition of C1/2 (C=sensitivityresponse time), linear models became asymptotically stable and the maximum allowed acceleration for remaining asymptotically stable decreased concurrently with the increased traffic density (k), but is irrelevant to the response time (T) of the vehicle. By contrast, the maximum allowed acceleration of the non-linear models decreased concurrently with increased traffic density and response time. Notably, the researchers found that the condition for the asymptotic stability of non-linear models was consistent to that of linear models (i.e. C1/2). Using Greenshields model as an example, the maximum allowed response time under various traffic densities can be expressed as Tmax=kj/(2ufk2), which is closely similar to the relaxation time equation of the high order continuum model. This similarity should be further examined.