This paper extends the results in [1] considering time delays in Standard Car Following models (CFMs). In [1], connected vehicles are characterized with CFMs models and controlled using linear string analysis to stabilize single-lane car following of human-driven vehicles (HDVs). In this paper, we revisit stability and safety conditions for traffic considering time delays due to lags in the input signals. We perform plant stability and string stability analysis to derive these conditions. Then we obtain the optimal number of HDVs that can be stabilized using one autonomous vehicle. Numerical simulations are provided to implement a case study on Intelligent Driver Model to discuss the influence of time delays that arise on HDVs and the autonomous vehicle on optimal number of HDVs that can be stabilized using one autonomous vehicle.

In this paper, we consider periodic communication delays within the connected autonomous vehicles platoon. Periodic signals are fundamentally simple to create, and in this study we analyze whether certain amplitude or frequencies can cause instability. This is important as we discover in this study, the classical method of replacing time-varying delays with constant delays does not capture the complex stability boundary of periodic time delays which could be exploited by attackers to cause instability in the vehicle platoon. We use the semi-discretization method to obtain plant stability. Then, we take the average value of the time delay functions to characterize the maximal admissible delay region such that the time-delayed system remains stable and provide string stability analysis. Through numerical simulations, we verify the analytical results. We construct stability charts in different parameter spaces to explore the effects of the model parameters on the system stability. A specific range of frequencies was found that could destabilize the connected autonomous vehicle platoon.