In order to avoid accidents drivers must maintain an adequate amount of separating distance between themselves and vehicles in front of them. If the driver of the lead vehicle suddenly applies his brakes, the driver of the following vehicle needs sufficient time and space to react and apply his brakes to come to a stop. If all vehicles and drivers had the same brake performance, then the required separating distance would simply be the distance traveled while reacting; basically the product of the speed being traveled times the reaction time of the driver. This simple rule would guarantee that a following driver would be able to apply his brakes before arriving at the place on the road where the lead driver applied his brakes. In real life though, all vehicle and drivers do not have the same stopping performance. There are variations due to the different tires on the vehicles, the brake balance of the vehicles, the reaction rates of the drivers, the skills of the drivers, and the traction afforded by the particular wheel paths followed by the vehicles. One way to deal with these variations is to use probability theory [2–6]. In this paper probability theory is used to determine how following distance should vary as a function of speed, average road friction, and variation of the road friction, so that the probability of a collision remains below a desired threshold.
