We have clues that suggests that it worked quite well sometimes even in period of troubles. The main problem is that some maritime routes are impossible at some time of the year. You can only sail from Rome to Alexandria during half of the year and vice versa. In addition the winter month were considered too dangerous so it narrows it to something like 4 months of navigation per year in one direction. Of course that's for trade, if you follow the coast and use row instead you would be able to travel much slowly but would still end up in Egypt. One good example is the head of a statue in the museum of Brussels. It's an emperor that reigned for a few month during the 3rd century crisis, but we still have a head found in Thessalonica. The only possible explanation is that a model of his head (that would be put on a generic statue body) was made immediatly after is accession to the imperial throne and sent to the provinces where it was copied to show the official portrait of the ruler.

So the boat was the most important element but the roman road system was equipped with relays that would enable the imperial postmen to change horses and continue their travel.

One funny thing on the subject is ORBIS a travel device for the roman empire made by the university of Stanford, quite useful for time travelers.