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 4 minutes. The average length of the queue Lq is
A) 0.4
B) 0.133
C) 4.167
D) 4.583
E) 6

Question

Quizplus · Accepted Answer

We can use the M/D/1 formula to find the average length of the queue Lq:

Lq = (λ^2 * T^2 + λ) / (2 * (1 - λ * T))

where λ = arrival rate = 1/10 per minute and T = service time = 4 minutes.

Plugging in these values, we get:

Lq = ((1/10)^2 * 4^2 + 1/10) / (2 * (1 - 1/10 * 4)) 
   = (1/25 + 1/10) / (2/5) 
   = 0.133

Therefore, the average length of the queue Lq is 0.133 or approximately 0.13 units. So the answer is B.

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