To be honest, I have never heard the terms "compound" or "absolute" gerund, but I think I can guess from your example. First, though, your example is incorrect because "having (been) tired" is a state or feeling and if that feeling has passed ("having been" means it happened already) it doesn't make sense that he would sit on the road, so "Being tired", or better, just "tired, he sat on the road" is o.k. However, it IS NOT a gerund! "Having been tired" or "being tired" are reduced adverb clauses: Because he was tired (adverb clause), he sat on the road. Gerunds act as subjects or objects, but not clauses.
Anyway, "Swimming (GERUND) is fun" is perhaps an absolute gerund and "Swimming in the river (GERUND + prepositional phrase) is fun" is perhaps a compound gerund.
Hope that helps!