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Part CCSIR NET December 2023mm1-formulas

Mm1 formulas

Consider an M/M/1 queue with arrival rate λ=15\lambda = 15 per hour and service rate μ=45\mu = 45 per hour. Let N(t) be the number of customers in the system at time t, and T1,T2T_{1}, T_{2} the time a customer spends in the queue and in the system. Which of the following statements are true?

  1. A.limt→∞lim_{t\to\infty} P(N(t) = 1) = 2/9✓ Correct
  2. B.P(T1>0)=1/3P(T_{1} > 0) = 1/3✓ Correct
  3. C.E(T1)=1/90E(T_{1}) = 1/90✓ Correct
  4. D.E(T2)=1/35E(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.

Drill statements like this

Related counterexample: An irreducible chain with a stationary distribution converges to it

More on this topic

The chapter behind this: Markov chains: classification and stationary behaviour — free to read

From Limit Theorems and Markov Chains › Markov chains: classification of states, stationary distributions

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