Accurate traffic demand estimation is critical for dynamic evaluation and optimization of signalized intersections. Existing studies based on connected vehicle (CV) data are designed for single phase only and are not well studied for real-time traffic demand estimation for supersaturated traffic conditions. Therefore, in this study, we propose a simultaneous multi-step traffic demand estimation method for each cycle based on his CV data considering both supersaturated and supersaturated traffic conditions at signalized intersections. First, a joint weighted likelihood function of the traffic demands of multiple phases is derived considering the real-time observed CV trajectories. This relaxes the first-in-first-out assumption by considering the initial queue and treating each queued CV as an independent observation. We then use the historical CV sample size to derive the joint prior distribution of traffic demand. Finally, a joint estimation method based on maximum posterior probability (that is, the JO-MAP method) was developed for cycle-based multi-step traffic demand estimation. The proposed method is evaluated using both simulation and empirical data. Simulation results show that the proposed method can produce reliable estimates under various penetration rates, arrival patterns, and traffic demands. The joint estimation feature relaxes our method’s demands on the penetrance of CVs, and considering the priors significantly improves the estimation accuracy. Empirical results show that the proposed method achieves accurate cycle-based traffic demand estimation with 12.73% MAPE, outperforming the other four of his methods.
