A priority waiting system assigns arriving customers one of four classes $($class $1$ has the highest priority$).$ Arrival rates of the classes have Poisson distribution and their average are:

Class Average Arrivals per Hour

$12$

$25$

$32$

$43$

Four servers process the customers, and each can handle an average of four customers per hour. The service rate is Poisson. Refer to the Table$18-4$ for Lq values.

a$.$ What is the server utilization? $($Round the final answer to $2$ decimal places.$)$

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? $($Do not round intermediate calculations. Round the final answers to $3$ decimal places.$)$

Class Average wait time Length of the wait line

$1$

hour

$2$

hour

$3$

hour

$4$

hour

c$.$ If the average arrival rate of the second priority class could be reduced to four customers per hour by shifting some arrivals into the third priority class $($which makes its average arrival rate $3$ per hour$),$ how would your answers to part b change? $($Do not round intermediate calculations. Round the final answers to $3$ decimal places.$)$

Class Average wait time Length of the wait line

$1$

hour

$2$

hour

$3$

hour

$4$

hour

d$.$ Explain why the impact of reassigning customers in part c is much less in this case?

multiple choice

Because the system utilization is lower.

Because the system utilization is higher.