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Sagot :
Answer:
9.587 ; 22.83 ; 25 minutes
Step-by-step explanation:
Given that:
Arrival rate (λ) = 0.42 trucks/ min
Service rate (μ) = 0.46 trucks / min
Trucks arrive at the weigh station at a rate of 0.42 trucks/min, and the station can weigh, on the average, 0.46 trucks/min. Determine the following:
a. Average number of trucks waiting in the queue, Lq
Lq = λ² / μ(μ - λ)
Lq = 0.42² / 0.46(0.46 - 0.42)
Lq = 0.1764 / 0.0184
= 9.5869565
= 9.587
b. Average waiting time in the queue for each truck, Wq
Wq = λ / μ(μ - λ)
Wq = 0.42 / 0.46(0.46 - 0.42) = 22.83 minutes
c. Average time spent in the system by each truck, W
W = 1 / (μ - λ)
W = 1 / (0.46 - 0.42)
W = 1 / 0.04
W = 25 minutes
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