  The erratic nature of human driving tends to trigger undesired waves that
amplify as successive driver reactions propagate from the errant vehicle to
vehicles upstream. Known as phantom jams, this phenomenon has been identified
in the literature as one of the main causes of traffic congestion. This paper
is based on the premise that vehicle automation and connectivity can help
mitigate such jams. In the paper, we design a controller for use in a connected
and autonomous vehicle (CAV) to stabilize the flow of human-driven vehicles
(HDVs) that are upstream of the CAV, and consequently to lower collision risk
in the upstream traffic environment. In modeling the HDV dynamics in the mixed
traffic stream, we duly consider HDV driver heterogeneity and the time delays
associated with their perception reaction time. We can find that the maximum
number of HDVs that a CAV can stabilize is lower when human drivers potential
time delay and heterogeneity are considered, compared to the scenario where
such are not considered. This result suggests that heterogeneity and time delay
in HDV behavior impairs the CAVs capability to stabilize traffic. Therefore, in
designing CAV controllers for traffic stabilization, it is essential to
consider such uncertainty-related conditions. In our demonstration, we also
show that the designed controller can significantly improve both the stability
of the mixed traffic stream and the safety of both CAVs and HDVs in the stream.
The results are useful for real-time calibration of the model parameters that
characterize HDV movements in the mixed stream.
