Question

Students arrive at the Administrative Services Office at an average of one every 12 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. Required:

What percentage of time is Judy idle? (Round your answer to 2 decimal places. Omit the % sign in your response.)

Answer 1

To find the percentage of time Judy is idle, calculate the average time between arrivals and the average service time. Then, determine the ratio of time between arrivals to the total service time, multiplied by 100, to find the percentage of time Judy is idle.

Step-by-step explanation:

To find the percentage of time Judy is idle, we need to calculate the average time between arrivals and the average service time.

Given that one customer arrives every 12 minutes on average, we can calculate the arrival rate per minute by dividing 60 by 12, which is 5 customers per minute. This means the average time between arrivals is 1/5 minutes, or 0.2 minutes.

The average service time is given as 10 minutes.

To calculate the percentage of time Judy is idle, we need to determine the ratio of time between arrivals to the total service time, multiplied by 100. The idle time is the time between arrivals minus the service time, which is 0.2 - 10 = -9.8 minutes, but since Judy cannot be idle for a negative amount of time, we set it to 0.

The percentage of time Judy is idle can be calculated as (idle time / total time) x 100, which is (0 / (0.2)) x 100 = 0%.