Part CCSIR NET June 2025p-zero-is-1-minus-rho-the-idle-probability-not-rho-itself

P zero is 1 minus rho the idle probability not rho itself

Consider the M/M/1 queue in which customers arrive according to a Poisson process with rate 3 and successive service times are independent exponential random variables having mean 1/9. Let $P_{n}$ be the long run probability that there are exactly n customers in the system. Then, which of the following statements are true?

A. $P_{0} = 1/3$
B. $P_{1} = 2/9$ ✓
C.The average number of customers in the system is 1
D.The average amount of time that a customer spends in the system is 1/6✓

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.

Drill statements like this

P zero is 1 minus rho the idle probability not rho itself

More on this topic