Customers arriving at a service centre are assigned one of three categories (1, 2, and 3); category 1 is 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 an average rate of five per hour. Arrival and service rates can be described by Poisson distributions.
a. What is the utilization of a server?
b. Determine the average wait time for customers in each class.
c. Find the average number of customers in each class that are waiting for service.