If the average waiting time for a customer in a system is 30 minutes and the customer service rate is 5 customers per minute,the average time a customer spends in the queue is ________.
A)35 minutes 48 seconds
B)25 minutes
C)29 minutes 48 seconds
D)30 minutes

Question

Quizplus · Accepted Answer

We can use the formula for the average waiting time in a queue:

Avg. waiting time = (Avg. queue length) / (Service rate)

Since we know the service rate is 5 customers per minute, we can solve for the average queue length:

Avg. queue length = (Avg. waiting time) x (Service rate)
                  = (30 min) x (5 customers/min)
                  = 150 customers

Now, we can use Little's Law to find the average time a customer spends in the queue:

Avg. time in queue = Avg. queue length / Arrival rate

We don't know the arrival rate, but we can use the fact that on average, there are 5 customers in the system (either being served or waiting in the queue) at any given time. So the arrival rate must be equal to the service rate:

Arrival rate = Service rate = 5 customers/min

Plugging in the numbers, we get:

Avg. time in queue = (Avg. queue length) / (Arrival rate)
                   = 150 / 5
                   = 30 minutes

Therefore, the answer is choice C, 29 minutes 48 seconds, since it's closest to 30 minutes.

If the Average Waiting Time for a Customer in a System