Traffic Oscillation using Stochastic Lagrangian Dynamics: Simulation and Mitigation via Control of Autonomous Vehicles

The phenomenon of stop-and-go waves is frequently observed in congested traffic. With the development of connected and autonomous vehicle (CAV) technologies, it is possible to reduce traffic oscillation via control of CAVs in a mixed traffic flow with both human drivers and autonomous vehicles (AVs). This paper introduces a stochastic Lagrangian model which is capable of simulating stop-and-go traffic considering the heterogeneity of drivers. The sample paths of the stochastic process are smooth without aggressive oscillation. The model is further extended to the mixed traffic flow condition, considering stochastic human driving behavior and deterministic behavior of AVs. With the proposed model, the variation of performance of AV control strategies can be quantified in addition to the average performance. A numerical example with a single lane circular road is used to investigate the impact of the AV control strategy on mitigating stop-and-go waves. Both qualitative and quantitative results show that the phenomenon of stop-and-go waves can be reduced significantly with only one AV, while the increase of AVs from 10% (two AVs) to 50% (10 AVs) offers just marginal improvement in relation to the ensemble-averaged performance and 95% confidence interval of the ensemble-averaged performance. The proposed simulation approach based on the stochastic Lagrangian model can effectively investigate the impact of AV control strategies on traffic oscillation, considering in particular the uncertainty of human driver behavior.