A single-phase waiting-line system meets the assumptions of constant service time or M/D/1.Units arrive at this system every 12 minutes on average.Service takes a constant 8 minutes.What is the average length of the queue Lq in units?
A)0.67
B)2.5
C)4.5
D)5.0
E)7.5

Question

Quizplus · Accepted Answer

In an M/D/1 queue, the average length of the queue Lq can be calculated using the formula Lq = (λ^2 * σ^2) / (2 * (1 - ρ)), where λ is the arrival rate, σ is the service time, and ρ is the utilization factor (λ * σ). Here, λ = 1/12 per minute, σ = 8 minutes, and ρ = (1/12) * 8 = 2/3. Plugging these values into the formula gives Lq = (1/12)^2 * 8^2 / (2 * (1 - 2/3)) = 0.67.

A Single-Phase Waiting-Line System Meets the Assumptions of Constant Service