A priority waiting system assigns arriving customers to one of four classes. Arrival rates (Poisson) of the classes are shown in the following table: Five servers process the customers, and each can handle three customers per hour.
Class Arrivals per Hour
1 .......... 2
2 .......... 4
3 .......... 3
4 .......... 2
a. What is the system utilization?
b. What is the average wait for service by customers in the various classes? How many are waiting in each class, on average?
c. If the arrival rate of the second priority class could be reduced to three units per hour by shifting some arrivals into the third priority class, how would your answers to part b change?
d. What observations can you make based on your answers to part c?