How many autonomous vehicles are required to stabilize traffic flow?
<|reference_start|>How many autonomous vehicles are required to stabilize traffic flow?: Collective behavior of human-driven vehicles (HVs) results in the well-known stop-and-go waves potentially leading to higher fuel consumption and emissions. This letter investigates the stabilization of traffic flow via a minimum number of autonomous vehicles (AVs) subject to constraints on the control parameters. The unconstrained scenario has been well-studied in recent studies. The main motivation to investigate the constrained scenario is that, in reality, lower and upper bounds exist on the control parameters. For the constrained scenario, we optimally find the minimum number of required AVs (via computing the optimal lower bound on the AV penetration rate) to stabilize traffic flow for a given number of HVs. As an immediate consequence, we conclude that for a given number of AVs, the number of HVs in the stabilized traffic flow cannot be arbitrarily large in the constrained scenario unlike the unconstrained scenario studied in the literature. Using nonlinear optimization techniques, we systematically propose a procedure to compute the optimal lower bound on the AV penetration rate. Finally, we validate the theoretical results via numerical simulations. Numerical simulations suggest that by enlarging the constraint intervals, a smaller optimal lower bound on the AV penetration rate is attainable. However, it leads to a slower transient response due to a dominant pole closer to the origin.<|reference_end|>
@article{bahavarnia2024how,
    title={How many autonomous vehicles are required to stabilize traffic flow?},
    author={MirSaleh Bahavarnia and Ahmad F. Taha},
    journal={arXiv preprint arXiv:2408.11212},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11212},
    primaryClass={eess.SY cs.SY}
}