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so the unit for Utilization in your example is "active request" ?

I just wish the article didn't assume units are easily inferred which would imply most readers are familiar with the subject.

Having read it more than once now I think utilization is a ratio, maybe?

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.

Yes, that's normally how utilisation is understood - as the fraction of time used by requests, which is therefore a dimensionless quantity.