Customers arriving at a service center are assigned to one of three categories, with category 1 given the highest priority. Records indicate that an average of nine customers arrive per hour and that one-third are assigned to each category. There are two servers, and each can process customers at the rate of five per hour. Arrival and service rates can be described by Poisson distributions.
a. What is the utilization rate for this system?
b. Determine the average waiting time for units in each class.
c. Find the average number of customers in each class that are waiting for service.