A waiting-line system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, the probability of more than two units in the system is approximately
A) zero
B) 0.015625
C) 0.0625
D) 0.25
E) 0.9375

Question

Quizplus · Accepted Answer

The probability of more than two units in the system (P(n > 2)) for an M/M/1 queue can be calculated using the formula P(n > 2) = (1 - ρ) * ρ^3, where ρ = λ/μ. Given λ = 1 and μ = 4, ρ = 1/4. Therefore, P(n > 2) = (1 - 1/4) * (1/4)^3 = 0.75 * 1/64 = 0.015625.

A Waiting-Line System That Meets the Assumptions of M/M/1 Has