Part CCSIR NET December 2023mm1-formulas

Mm1 formulas

Consider an M/M/1 queue with arrival rate $λ = 15$ per hour and service rate $μ = 45$ per hour. Let N(t) be the number of customers in the system at time t, and $T_{1}, T_{2}$ the time a customer spends in the queue and in the system. Which of the following statements are true?

A. $l i m_{t \to \infty}$ P(N(t) = 1) = 2/9✓
B. $P (T_{1} > 0) = 1/3$ ✓
C. $E (T_{1}) = 1/90$ ✓
D. $E (T_{2}) = 1/35$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

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Mm1 formulas

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