Flying a Pitts S-2C in a circuit full of students is ahh, interesting! The aircraft does a circuit of around 2:15 mins - 30 secs to climb to downwind (climbing turn so you can see ahead); 1 min S&L on downwind; 30 secs base and final descending turn (2000 fpm descent) so you can see the runway; then 15 secs for touch and go.
The Pitts has the gliding characteristics of a manhole cover, and having had one total engine failure and another partial (severe) loss of power, I will not fly further away from the runway than I know I can glide - which makes for very tight circuits at 1000' circuit height. At Camden (1000' AGL circuit heght) I could safely get down even if I come over the fence at 1000'.
Bearing in mind that we climb and descend faster (2000 to 2500 fpm) than just anything else in the circuit, we can usually safely cut off a couple of students on climbout; but it's very difficult to do less than 100kts on downwind without having the nose so high that we lose forward vis - which is not a good idea...So I gets lots of practice at go-arounds and overtaking on the inside of climbs or descents
Fly the circuit for your own aeroplane. If the turkey ahead of you is a student (with or without an instructor) who wants to turn circuits into a navigation exercise, don't let yourself get suckered into flying their circuit. Their engine failure would be their problem, but you'll be on your own with yours...