Trajectory planning at a signalized road section in a mixed traffic environment considering lane-changing of CAVs and stochasticity of HDVs

Connected and automated vehicles (CAVs) are projected to bring significant benefits to traffic efficiency and driving comfort. However, the realization of full CAV penetration rate will take a long time. In this paper, a framework is proposed for planning the trajectories of vehicles at a signalized road section in a mixed traffic environment consisting of CAVs, human-driven vehicles (HDVs) and connected and automated buses (CABs). In the proposed trajectory planning framework (TPF), both the lane-changing (LC) behavior of CAVs and the stochasticity of HDVs are considered. The whole TPF is composed of a planning module, a running module, and a switching module. In the planning module, the mixed integer programming (MIP) models for trajectory planning with/without LCs are formulated to optimize the trajectories of CAVs/CABs. A parsimonious algorithm is designed to determine a suitable planning time horizon for the MIP models. The running module and the switching module are designed to ensure the driving safety of vehicles. To consider the stochasticity of HDVs, the concept of alpha-trajectory is employed in simulations to produce predicted trajectories of HDVs, while the actual trajectories of HDVs are generated by a stochastic car-following model. Here, alpha is a parameter between 0 and 1 related to one randomly changing parameter of HDVs, and alpha-trajectory is a series of predicted trajectories generated for HDVs based on the value of alpha. A rolling time horizon scheme is applied for TPF to account for the time-varying traffic situations. Numerical experiments under different traffic states and market penetration rates (MPRs) of CAVs/CABs are conducted to validate the performance of the proposed TPF. The average improvement in travel time and fuel consumption can reach up to 28.9 %, 17.8 % and 52.2 %, 35.3 % under medium and heavy traffic, respectively, and the average improvement in driving comfort is over 20 % in most traffic scenarios. The comparison experiment without fixed rolling time window (FTW) shows the advantage of setting FTW in adapting to the time-varying traffic situations, especially under heavy traffic. The sensitivity analysis shows that the values of alpha 1 and alpha 2 associated with alpha-trajectory can affect the performance of the proposed TPF in varying degrees. Finally, the length of the control zone is suggested to be set to 300-500 m.