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Although connected vehicles (CVs) will soon go beyond testbeds, CVs and human-driven vehicles (HVs) will co-exist over a long period. Hence, it is critical to consider the interactions between these two types of vehicles in traffic flow modeling. In this study, we aim to develop a macroscopic model to understand how CVs would impact HVs in the traffic stream. Grounded on the second-order traffic flow model, we study the relationships among flow, density, and speed by two sets of formulations for the groups of CVs and HVs, respectively. A set of friction factors, which indicate CVs' impact to HVs, are introduced to the speed equation for accounting CV speed impacts. Then extended Kalman Filter is employed to update both model parameters and friction factors in real-time. By using CVs trajectory data as measurements, the difference between CV average speed and overall traffic mean speed will be fully accounted. The proposed model will serve as a basis for designing CV-based traffic control function,...Read more