How to Calculate service rate in M/M/1 queuing model in simevents with different server capacities.

I want to calculate service rate in M/M/1 queuing system in simevents with varying server capacities.

If I specify:

queue length to be inf.

Arrival rate as 8 entity/sec.

Service time as 9 entity/sec.

How do I calculate the value of : rho=lambda/mu.

Usually it will be 8/9.

if suppose server capacity is 2 or 3?

Then how to calculate service rate and value of rho(which is basically server utilization)

[Renato SL]

A few things:

1. 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.
2. 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.
3. 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.