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The math seems to be off in a few places:

1. When solving for the arrival rate λ, it should be λ=ρ/S instead of λ=S/ρ.

2. Calculating the arrival rate λ with the correct formula results in 9 requests/second instead of 10 request/second.

3. Calculating the new utilization ρ should be 0.05x9 instead of 0.05x10.

The result of the calculated utilization ρ is correct (0.45), so is the calculated new latency.

edit: new lines



Even with the wrong formula for λ This one is also off:

λ = S/ρ = 0.1/(1−0.9) = 10

Should be 1 not 10.




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