A waiting-line system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, what is the probability of less than two units in the system?
A) 0.0625
B) 0.25
C) 0.75
D) 0.9375
E) 1.00

Question

Quizplus · Accepted Answer

The probability of having less 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^2/(1-ρ), where ρ = λ/μ. Given λ = 1 and μ = 4, ρ = 1/4 = 0.25. Substituting ρ into the formula gives P(n < 2) = 1 - 0.25 - (0.25)^2/(1-0.25) = 1 - 0.25 - 0.0625/0.75 = 1 - 0.25 - 0.0833 = 0.9375.

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