Modelling and Simulating Several Time-Delay Mechanisms in Human and Automated Driving

Summary

In vehicular traffic, reactions to new traffic situations are subject to several mechanisms of time delay. Besides the reaction time of the drivers (or sensors), the finite acceleration capabilities lead to a nonzero “velocity adaptation time” to perform the action itself (e.g. changing the velocity). The commonly used explicit integration schemes for simulating the models introduce the update time as a third delay parameter. By means of numerical simulations with a time-continuous car-following model, we investigate how these times interplay with each other. We show that the three delay times give rise to two types of instabilities: The long-wavelength string instability is mainly driven by the velocity adaptation time while short-wavelength local instabilities arise for sufficiently high reaction and update times. We show that, with respect to stability, there is an ‘optimal’ adaptation time as a function of the reaction time and draw implications for human vs. semi-automated driving.