Optimizing the safety-efficiency balancing of automated vehicle car-following

•Explicit balancing of safety and efficiency to specify the car-following behavior of AVs.•Safety specified via crash-risk, severity-of-crash, and monetary-cost-of-crashes.•Efficiency specified via Value-of-Time, considering impacts on arrival time.•Numerical case study demonstrates tractability; intuitive sensitivity to stimulus.•Explicit balancing supports demonstrating that a duty of care has been met. This paper proposes an approach to rationally set automated vehicles’ car following behavior that explicitly balances between the competing considerations of safety (i.e. small probabilities of a high-consequence crash) and efficiency (guaranteed but small impacts on journey arrival time due to the choice of car following distance). The specification of safety and efficiency are both based on empirically supported concepts and data. In numerical analyses with empirical vehicle trajectories at two sites, we demonstrate intuitive response to systematic variation in numerical values selected as inputs, as well as whether the scope of the efficiency consideration is selfish or systemwide. The proposed balancing is aligned with the standard “Hand Rule” criterion to demonstrate that a duty of care has been met, in which a burden must be borne if it is less than the product of the probability of loss to a third party and the magnitude of loss. Thus the proposed approach is intended to be useful for designers of control algorithms for AVs to establish that they have met their duty of care, taking both safety and efficiency into account.