See this image for my train circle:

If the circle only has signals at the inputs/outputs, then there wouldn't be a problem: trains would queue up to use the circle and no more than one train would ever enter the circle. Restricting it that way doesn't allow two trains to pass each other at the same time, however, and will limit throughput in other ways. Adding four additional signals, as in the image, splits the circle into four semi-circles. Unfortunately, if four trains enter the circle near the same time, they can cause a gridlock situation. In fact, allowing any more than one train into the circle seems to allow a gridlock situation as far as I can tell.
Is there something that can be done to fix the gridlock scenario? Maybe different signal placements, or maybe adding some extra tracks? I'd prefer the circle to not get larger than it already is.