A priority waiting system assigns arriving customers one of four classes (class I has tire highest priority). Arrival rates of the classes have Poisson distribution and their average are:

Five servers process the customers, and each can handle an average of three customers per hour. The service rate is Poisson.
a. What is the server utilization?
b. What is the average wait time for service by customers in the various classes? How many are waiting in each class on average?
c. If the average arrival rate of the second priority class could be reduced to three customers per hour by shifting some arrivals into the third priority class (which makes its average arrival rate 4 per hour), how would your answers to part b change?
d. What observations can you make based on your answers to part c?

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Class Average Arrivals per Hour 2 3 4