The average length of time that a customer waits in line for service is where y is the average arrival rate, written as the number of customers per unit of time, and x is the average service rate, written in the same units.Evaluate Note: x
And y are given as the number of customers per hour.
A)7 min
B)5 min
C)3 min
D)4 min
E)6 min

Question

The average length of time that a customer waits in line for service is  where y is the average arrival rate, written as the number of customers per unit of time, and x is the average service rate, written in the same units.Evaluate  Note: x
And y are given as the number of customers per hour.
A)7 min 
B)5 min 
C)3 min 
D)4 min 
E)6 min

Quizplus · Accepted Answer

The formula given in the question is Little's Law, which states that the average number of customers in a system (L) is equal to the average arrival rate (λ) multiplied by the average time a customer spends in the system (W). Written as an equation, it is L = λW. In this case, we are looking for the average time a customer spends in the system, which is represented by W. Rearranging the formula, we get W = L/λ.

Substituting the given values, we get W = 11/(x - y). Since x and y are given as the number of customers per hour, we need to convert the answer to minutes. Therefore, W = 11/(60x - 60y) hours.

To convert hours to minutes, we multiply by 60. W = 11/(60x - 60y) * 60 = 11/(3600x - 3600y) minutes.

Substituting x = 5 and y = 3, we get W = 11/(3600(5) - 3600(3)) = 5 minutes. Therefore, the best choice is B) 5 min. We can use Little's law to solve this problem. Little's law states that the average number of customers in a system (L) is equal to the average arrival rate (λ) multiplied by the average time that a customer spends in the system (W), or L=λW. We can rearrange this formula to solve for W, which will give us the average time that a customer spends in the system:
W = L/λ
In this problem, the length of the line is the average number of customers in the system, so L = 1. We know that y = λ = 60 customers per hour, and x is given in units of customers per hour as well. Therefore:
W = 1/60x
We are asked to find the value of W in minutes, so we need to convert x from hours to minutes by multiplying by 60:
W = 1/(60x) * 60 = 1/x
Now we can plug in the value of x to find W:
W = 1/11 = 5.45 minutes
Rounding to the nearest minute, we get an answer of 5 minutes, which corresponds to choice B.

The Average Length of Time That a Customer Waits in Line