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. The average length of the queue L_q is approximately A) 0.67 B) 2.5 C) 4.5 D) 5.0 E) 7.5

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Quizplus · Accepted Answer

In an M/D/1 queue, the average queue length 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 ≈ 0.67.

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