Modeling and analysis of heterogeneous traffic flow considering dynamic information flow topology and driving behavioral characteristics

Connected vehicles (CVs) have demonstrated significant potential for addressing traffic issues. This paper presents a mathematical framework for stochastic heterogeneous traffic flow, integrating regular vehicles (RVs) and CVs, considering stochasticity, driver's dynamic time headway (DTH) characteristics, and the information flow topology (IFT) of CVs. We develop a novel car -following model (CFM) for RVs, accounting for both driver's stochasticity and DTH characteristics. Furthermore, we propose a dynamic model for CVs by integrating connected assisted driving strategies (CADS) into the RVs' model, which includes a dynamic information flow topology (DIFT) based on the time headway (TH) between vehicles within the communication range. We derive second -order exponential stability conditions for both RVs and CVs by employing the Lyapunov stochastic stability theory. We investigate the impact of driver stochasticity, DTH characteristics, and CADS on heterogeneous traffic flow characteristics through extensive numerical experiments. Model calibration results indicate that, in comparison to the state-of-the-art model, the proposed model exhibits superior prediction accuracy, achieving a 9.09% improvement at the group -driver level and a 10.47% improvement at the individual -driver level. Theoretical and numerical experimental results demonstrate that CVs with the proposed assisted driving strategy effectively mitigate traffic oscillations, and traffic flow stability improves as the CV penetration rate increases. Moreover, CVs can efficiently suppress stochasticity in traffic flow, with the strength of traffic fluctuations decreasing as the CV penetration rate grows. Different CV spatial distributions result in different propagation strengths of disturbances in traffic flow, adhering to a specific dual Gaussian distribution. Under various conditions, the average decline rates of speed fluctuations and energy consumption for traffic with the increasing CV penetration rate are 20%-50% and 10%-30%, respectively.