ESH. Your parents are TA because they should have gotten a cell phone a loooong time ago. There is no excuse not to get one.

YTA because you couldn't even wait 5 minutes for your parents. I think excluding your parents from this moment is far more inconsiderate than making your guests wait 15 minutes. Did you end up making every minute count, down to the last second? Do you think your guests would be there if they couldn't wait an extra 15 minutes? I doubt everyone present at the ceremony remained there for the entire duration.

Surely cutting 10-15 minutes of your limited time is worth the chance of sharing this moment with your parents, no matter the reason they are late. Was it worth having those extra minutes you paid for at the cost of excluding your parents from one of the most important moments in all your lives?