Why is arrival rate a function of service time?
replies(2):
When the theoretical service is optimized to take half a long, the assumption is that the request rate doesn't actually change. So they use the above relationship to calculate the new utilization, given half the service time and the same arrival rate.
I just wish the article didn't assume units are easily inferred which would imply most readers are familiar with the subject.
But that means the unit for S needs to be seconds/request such that:
utilization(ro) = S * arrival_rate(lambda) = seconds/request * request/seconds = bare ratio.
More coffee required.