Generally if it's just sleepy tired, then being out in the fresh air wakes me up, and it would be more likely that I would feel sleepy either just after lunch or in the evening. If it's physically exhausted, I probably would still cycle but much slower, and I would be aware my reaction times would be slower so I might try to adjust my route to avoid the bits where I felt I needed more concentration than I actually had.
As someone else said the worst thing for concentration is being emotionally upset/angry at something either on or off the bike. If something happens with a motorist, you need to not brood on it, you can do that at the end of the journey. When I do brood, I end up making more mistakes.