  The paper introduces a new bidirectional microscopic inviscid Adaptive Cruise
Control (ACC) model that uses only spacing information from the preceding and
following vehicles in order to select the proper control action to avoid
collisions and maintain a desired speed. KL estimates that guarantee uniform
convergence of the ACC model to the set of equilibria are provided. Moreover,
the corresponding macroscopic model is derived, consisting of a conservation
equation and a momentum equation that contains a nonlinear relaxation term. It
is shown that, if the density is sufficiently small, then the macroscopic model
has a solution that approaches exponentially the equilibrium speed (in the sup
norm) while the density converges exponentially to a traveling wave. Numerical
simulations are also provided, illustrating the properties of the microscopic
and macroscopic inviscid ACC models.
