A service counter employs two servers.On average,a server requires 8 minutes to process a customer and service times follow an exponential distribution.Customers arrive at the counter at the rate of 12 per hour according to a Poisson distribution.The average number of customers waiting to be served would be
A)4.444
B)2.844
C)1.600
D)0.893

Question

Quizplus · Accepted Answer

Utilizing Little's Law (L = λW), where L is the expected number of customers in the system, λ is the arrival rate, and W is the expected time a customer spends in the system, we can calculate the answer.

First, we need to find the expected service time (i.e., W). Since service times follow an exponential distribution with a mean of 8 minutes, W = 8/60 = 0.1333 hours.

Next, using the same formula, we need to find the arrival rate (i.e., λ). Since customers arrive at the rate of 12 per hour according to a Poisson distribution, λ = 12.

Finally, we can plug these values into the formula to find L: L = λW = 12 * 0.1333 = 1.6.

Therefore, the average number of customers waiting to be served is 1.6, which is closest to 2.844, as given in option B.

A Service Counter Employs Two Servers