Part CCSIR NET December 2025with-2-servers-the-death-rate-caps-at-2-mu-once-both-servers-are-busy-it-does-not-keep-scaling-with-n

With 2 servers the death rate caps at 2 mu once both servers are busy it does not keep scaling with n

Consider an M/M/2 queuing system with the birth rate $\lambda=4$ per minute, the death rate $\mu=1$ per minute, and the total capacity of 3 customers (including the ones that are being served). Let $p_{0}$ and $p_{3}$ denote the long-run probabilities that the system will be empty (i.e. without customers) and will be blocked (i.e. full), respectively. Which of the following statements are true?

A. $p_{0}+p_{3} = 17/29$ ✓
B. $p_{0} > p_{3}$
C. $p_{3}/p_{0} = 2$
D. $p_{3}-p_{0} = 15/29$ ✓

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.

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With 2 servers the death rate caps at 2 mu once both servers are busy it does not keep scaling with n

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