In queuing theory, what is the difference between departure rate and service rate? As per my understanding, a job departs as soon as it's servicing is over and thus they should be same. However, I came across the following statement: _The throughput for a queuing system with infinite capacity is the mean number of customers processed in a unit of time, i.e. the departure rate. Since the departure rate is equal to the arrival rate (and assuming ρ < 1), the throughput is λ = m · ρ · µ:_ where m is the number of systems. So I am guessing departure rate and service rates are different. How to distinguish between the two? the description says _mean number of customers processed in a unit of time_ which is also similar to what service rate means. 1 page 8 is where it is mentioned.

The service rate is the number of customers per hour that the server can process, assuming there are always more customers waiting. It doesn’t depend on the arrival rate. So if the service rate is 10/hour, it means the server _could_ process 10 per hour (on average of course), but sometimes there won’t be customers who need processing, so the server will process fewer.

Departure rate is the number of customers leaving the system. So if 8 customers per arrive on average, then 8 customers per hour will depart on average (assuming $\rho < 1$, i.e., the system is stable), as noted by Math1000 in one of the comments.

The reason the departure and arrival rates are equal is that the system does not create or destroy customers — every customer that enters also departs, and vice versa.