  This study develops the headway control framework in a fully automated road
network, as we believe headway of Automated Vehicles (AVs) is another
influencing factor to traffic dynamics in addition to conventional vehicle
behaviors (e.g. route and departure time choices). Specifically, we aim to
search for the optimal time headway between AVs on each link that achieves the
network-wide system optimal dynamic traffic assignment (SO-DTA). To this end,
the headway-dependent fundamental diagram (HFD) and headway-dependent double
queue model (HDQ) are developed to model the effect of dynamic headway on
roads, and a dynamic network model is built. It is rigorously proved that the
minimum headway could always achieve SO-DTA, yet the optimal headway is
non-unique. Motivated by these two findings, this study defines a novel concept
of maximin headway, which is the largest headway that still achieves SO-DTA in
the network. Mathematical properties regarding maximin headway are analyzed and
an efficient solution algorithm is developed. Numerical experiments on both a
small and large network verify the effectiveness of the maximin headway control
framework as well as the properties of maximin headway. This study sheds light
on deriving the desired solution among the non-unique solutions in SO-DTA and
provides implications regarding the safety margin of AVs under SO-DTA.
