ITPEC FE Subject A April 2026 Question 3
ITPEC FE Subject A April 2026 — Question 3 of 60
Utilization is defined as the mean arrival rate divided by the mean service rate.
It is written ρ = λ / μ, where λ is the mean arrival rate and μ is the mean service rate. It expresses the fraction of time the server is busy:
- •
ρ < 1— the server keeps up and the queue stays finite - •
ρclose to 1 — waiting time grows sharply - •
ρ ≥ 1— arrivals outpace service and the queue grows without bound
Answer (a)
Why not others:
- (b) Average inter-arrival time — the reciprocal of the arrival rate (1/λ); that is a time, not a ratio of two rates
- (c) Average service time — the reciprocal of the service rate (1/μ), also a time
- (d) Average retention number — not a standard queuing-theory quantity
Key rule: Utilization is dimensionless because it divides a rate by a rate. Anything described as an average time is the reciprocal of a rate instead.
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