Antioch was a great commercial centre in its heyday and a far cry from the soap and leather-focused provincial backwater that Antakya had become. To get an idea of the intense interchange of goods between Antioch and the rest of the Roman Empire and beyond, the best source is Commercial Syria under the Roman Empire by Louis C. West in Transactions and Proceedings of the American Philological Association (Vol. 55 1924, pp. 159-189) Despite the work being amazingly detailed and encompassing, the one thing that author does not discuss is how the goods moved around.
The map below shows the chief trade routes of the Syrian region of the Roman Empire.
Antioch in its heyday was one of the chief entrepots of the Roman Empire as far as the China trade was concerned. Friedrich Hirth is his book, China and the Roman Orient, researches into their ancient and medieval relations. as represented in old Chinese records. Leipzig, 1885 sheds a totally new light on the Antioch story because he finds references to Chinese visitors who made it to the Roman Orient and carried back their views of what they had seen and put them to paper. An important component of this trade was silk, which arrived in Antioch and was then sent down to the Lebanese coast which was the main production centre for Tyrian Purple dyes for silk.