  Accurate traffic demand estimation is critical for the dynamic evaluation and
optimization of signalized intersections. Existing studies based on connected
vehicle (CV) data are designed for a single phase only and have not
sufficiently studied the real-time traffic demand estimation for oversaturated
traffic conditions. Therefore, this study proposes a cycle-by-cycle multi-phase
traffic demand joint estimation method at signalized intersections based on CV
data that considers both undersaturated and oversaturated traffic conditions.
First, a joint weighted likelihood function of traffic demands for multiple
phases is derived given real-time observed CV trajectories, which considers the
initial queue and relaxes the first-in-first-out assumption by treating each
queued CV as an independent observation. Then, the sample size of the
historical CVs is used to derive a joint prior distribution of traffic demands.
Ultimately, a joint estimation method based on the maximum a posteriori (i.e.,
the JO-MAP method) is developed for cycle-based multi-phase traffic demand
estimation. The proposed method is evaluated using both simulation and
empirical data. Simulation results indicate that the proposed method can
produce reliable estimates under different penetration rates, arrival patterns,
and traffic demands. The feature of joint estimation makes our method less
demanding for the penetration rate of CVs and the consideration of prior
distribution can significantly improve the estimation accuracy. Empirical
results show that the proposed method achieves accurate cycle-based traffic
demand estimation with a MAPE of 12.73%, outperforming the other four methods.
