Fast Passing Rules
When you are traveling along the Imperial Roads, there is a complicated structure of competing protocols for who has the right of way. But when you are as big as a Circus, all you really need to know is that Dragon Army and Nobles can punt you off the road any time they want- but everyone else will mostly get out of your way.
The trick is encouraging Nobles and military to yield the right of way to you.
With Nobles, this is usually easy. You have one or two riders ahead of the Circus, in full costume. They make sure that everyone knows that the Circus is coming, and that the Circus is on parade. They have trumpets. Two soundings means that a VIP is approaching, and that everyone should be prepared to put on their best show. One sounding means that trouble is afoot.
Next come several large animals. Elephants are best. These make it clear to any approaching nobles that you are a real Circus, not some highway robbers or uppity merchants. The animals also highlight the fact that moving the Circus off the road is going to be slow. So slow, in fact, that the Nobles must surely rather rest and enjoy the parade instead. Once the reality of the Circus becomes clear, the front riders can offer the Nobles a tea service. Perhaps with a fine tent to keep off the afternoon sun. You won't have time to put up a real tent, so you need some comely ladies or not-so-grubby children to balance the tent poles. You don't want anyone on tent duty who might scare the Nobles, or their guards. If it is windy, you'd better skip the tent. Pull a wagon over to provide some shelter from the wind, instead.
Set the Nobles off to one side of the road. Always the right (eating hand) side of the road. That way, you only have to keep one side of your wagons looking good when you are pressed for time. Make sure that everyone gives a little performance as they pass the Nobles. Nothing too long; we don't want to actually stop. So each act should cut to the best thing they've got that they can do from a wagon, or while standing still for less than a minute on a road. Don't worry about spoilers; the Nobles are heading to someplace you've already been.
Then, parade finished, roll up the tent and run it back up the front of the Circus for the next Noble.
There a few other complications. Show horses aren't accustomed to being ridden all day, so you need to swap them out. If the Cook runs out of something, you need to make sure that the outriders don't offer it any more. But with a little attention to detail, it usually works out.
The military isn't much different, but they usually have deadlines. So sometimes it will work, sometimes it won't. You offer tea to the officers, and you encourage the ladies to tease a little more with the soldiers. Basically, make sure that everyone has a good time, and they'll be more inclined to cede the right of way to you next time.