A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 10 minutes on average. Service takes a constant 6 minutes. What is the average length of the queue, L_q, in units? A) 0.450 B) 0.133 C) 4.167 D) -2.083 E) 6

Question

Quizplus · Accepted Answer

In an M/D/1 queue, Lq = (λ^2 * σ^2) / (2 * (1 - ρ)), where λ = 1/10, μ = 1/6, ρ = λ/μ = 0.6, and σ^2 = 0. Therefore, Lq = (0.1^2 * 0) / (2 * (1 - 0.6)) = 0.45.

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