My curiosity was piqued when I read that Philip V of Macedon was threatening to assist Hannibal during the Second Punic War. How quickly could information about defeats, victories, or other setbacks have reached him or other players in the region in that time?
Someone asked a similar question recently, you might find the answers you're looking for there! https://www.reddit.com/r/AskHistorians/comments/69gw2v/im_a_roman_emperor_ruling_in_rome_the_persians/
I'll also take another opportunity to plug the Stanford University Orbis project: http://orbis.stanford.edu/