Question

A single computer arrives at a refurbishing station every 100 minutes on average following a Poison distribution. The computers are processed at a mean rate of 1:3 per hour, following an exponential distribution

a) What is the average number of computers in the system?
b, What is the average time a computers spends from when it arrives until it's refurbishing begins?
c) On average, what percentage of time is refurbishing actually being performed?

Answer 1

λ = 1/(100/60) = 0.6 per hour, μ = 1.3 per hour

(a) L = λ/(μ - λ) = 0.6/(1.3 - 0.6) = 0.857

(b) Wq = λ/[μ(μ - λ)] = 0.6/[1.3(1.3 - 0.6)] = 0.659 hours (39.6 minutes)

(c) ρ = λ/μ = 0.6/1.3 = 0.4615 (46.15%)