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CMA Intermediate · Operations Management and Strategic Management · Scheduling and Queuing Models

For an M/M/s queue with s = 2, λ = 6 per hour and μ = 4 per hour per channel, which of the following is the correct value of P0 using P0 = 1 / [Σ(n=0 to s−1) (λ/μ)^n/n! + (λ/μ)^s/(s!(1−ρ))]?

P0 equals 1/7. The sum of the first terms is 1 + 1.5 = 2.5, and the final term is 2.25 divided by 2 × 0.25, which is 4.5. The total is 7, so the probability of an empty system is 1/7.

  1. A1/7Correct
  2. B1/5
  3. C1/9
  4. D1/4

Explanation

λ/μ = 1.5, ρ = 0.75. Sum for n=0 to 1 = 1 + 1.5 = 2.5. Last term = 2.25/(2 × 0.25) = 4.5. Total = 7.0, so P0 = 1/7. Using (1−ρ) omitted gives 2.5 + 1.125 = 3.625, a wrong result.

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