Combining shockwave analysis and Bayesian Network for traffic parameter estimation at signalized intersections considering queue spillback

This paper focuses on traffic parameters estimation at signalized intersections based on a framework combining shockwave analysis (SA) and Bayesian Network (BN) using vehicle trajectory data. Detailed queuing evolution and spillback across adjacent intersections are considered. According to shockwave analysis, the analytical probability distribution of individual vehicle's travel time is derived based on different initial conditions. This probability distribution is parameterized by the fundamental diagram (FD) parameters, traffic volume, and cycle state (queue length). A three-layer recursive BN model is then proposed to construct the state evolution process as well as the relationships between traffic volume, cycle state, FD parameters, sampled vehicles' arrival times and intersection travel times. As traffic volume and initial queue cannot be measured directly from sampled trajectory data, the expectation maximization (EM) algorithm and particle filtering (PF) are introduced to solve this recursive BN model. By shockwave analysis, such estimated traffic parameters are then used to estimate the maximum queue length and traffic volume of each cycle. The proposed method is evaluated using microscopic traffic simulation data as well as empirical data. Numerical results show that the proposed method achieves promising accuracy even under low penetration rates, with the mean absolute percentage error (MAPE) of the estimation bounded by 15% and generally around 10%.