A few things:
- I think what you described as service time is actually the service rate, which is 9 entity/sec in your case. The service time should be 1/9 sec/entity (it is service time, so the unit should be a time unit). That should answer your question about service time/service rate.
- You mentioned the formula of rho, which I think is correct, so indeed you can use that formula. But your wording of "Usually it will be 8/9" might be misleading. It is 8/9, not just usually.
- Regarding the variable server capacity, I think it is called a M/M/c model. I browsed about it just now. There are a lot of references, so I believe you should find one easily.
