complex motions along a path

For a project for work, I am trying to create an animation of a traffic roundabout - sometimes called a traffic circle - used to control traffic at an intersection without a traffic light. This particular roundabout is at the intersection of three roads, so imagine an "O" with roads intersecting at noon, 3 p.m., and 6 p.m. positions.

The looping animation I have in mind would involve an arrow, representing a vehicle, moving along a path simulating a road. It would travel along the road, enter the traffic circle and exit at either of the two other roads and carry on along the rest of the path. What I am trying to do is find an easy way to randomize the paths of the arrow, so that the looping animation is seamless. One arrow, for example, would enter at the noon position, loop around and exit at the 3 p.m. road; the next would exit at the 6 p.m.  And of course, there would be a separate animation of opposite traffic entering at the 6 p.m. road and alternatively exiting at the 3 p.m. and 9 p.m. intersections.  Any ideas on how to do this will be greatly appreciated. I am also unsure whether AE or Animate may be the best Adobe products for this animation.