Suppose your company has a simple service process. Customers arrive at the rate of 48 per hour. They are currently served at the rate of 60 per hour.
a) Compute the utilization, average time a customer spends waiting for service to begin, and the average number of people in the system.
b) The numbers above are long-term averages. At any given time, the number of people in the system may be more or less than your computed average. The company believes that when there are more than 10 people in the system, customer satisfaction drops significantly. What percentage of time are there more than 10 people in the system? Hint: you can solve this by computing the probability of exactly 0 people in the system, the probability of exactly 1 person in the system and so on up to the probability of exactly 10 people in the system. The sum of these values gives the probability of 10 or fewer people in the system. Once you have that, you can easily get the probability of more than 10 people in the system.