Another simple solution that none of us seem to do.

If you want to avoid patients being angry about being kept waiting 

Either:

1.      Don’t keep them waiting and make sure your clinics always run on time (difficult)

or

2.      Let them know you are overrunning and give them an idea of how long (simple)

I think many of us are afraid to confront the issue and hide behind an air of business and importance, rather than thinking about it from the patient’s point of view.