Are current microscopic traffic models capable of generating jerk profile consistent with real world observations?

Microscopic behavior modeling plays a critical role in traffic flow analyais, simulation, and autonomous vehicle algorithm development. Numerous efforts are devoted to the development of it in both longitudinal and lateral dimensions. Empirical observations reveal that jerk (the differential of acceleration) significantly influences traffic safety, with a speed-dependent jerk profile observed in both longitudinal and lateral movements. Replication of the speed-dependent jerk profile is crucial when the microscopic models are employed to the analysis of traffic safety. However, this research shows that current stochastic microscopic models cannot describe speed-dependent jerks, and thus cannot be directly used to describe driving behavior with considerable jerk profiles. This research firstly derives the jerk distribution for a general stochastic car following (CF) model, and then shows that several CF models together with lateral movement model cannot generate the realistic jerk distribution. A compound Poisson formulation is proposed to remedy the drawbacks of these models. The model consists of a diffusion part and a jump part. The former describes normal driving stochasticity, while the latter describes driving involving high jerk. The numerical studies show that the proposed model can replicate the speed-dependent jerk phenomenon. The propagation of the behavior in the traffic flow is also investigated.