We address the challenge of how to share the limited wireless channel capacity for the
exchange of safety-related information in a fully deployed vehicular ad hoc network (VANET).
In particular, we study the situation that arises when the number of nodes sending periodic
safety messages is too high in a specific area. In order to achieve a good performance of
safety-related protocols, we propose to limit the load sent to the channel using a strict
fairness criterion among the nodes. A formal definition of this problem is presented in terms
of a max-min optimization problem with an extra condition on per-node maximality.
Furthermore, we propose FPAV, a power control algorithm which finds the optimum
transmission range of every node, and formally prove its validity under idealistic conditions.
Simulations are performed to visualize the result of FPAV in a couple of road situations.
Finally, we discuss the issues that must be taken into account when implementing FPAV.