Continuous and Discrete Analysis of Local Stability for Car-Following Model With Speed-Based Desired-Headway

Stability is a critical issue of traffic dynamics to decode disturbance propagation and to avoid traffic fluctuation or congestion. This research, based on a simplified linear CFM with desired headway proportional to vehicle speed, targets at the process where the following car evolves to local stability, i.e. equilibrium state, with differential and difference equation systems for continuous and discrete analysis, respectively. Concerning continuous CFM, it is found that vehicles always achieve local stability, as long as the speed of the preceding vehicle is smaller than the limit, resulting in larger stability region compared to existing research. In contrast, stability from the discrete CFM is conditional on reaction time, and as reaction time decreases, the stable region increases. This research may promote stable, safe, and fatigue-free driving behaviors, provide insights to simple driving controller, and lay foundation to vehicular automation.