$3$

$8$ coss

ecose

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

$\backslash$table$[[$Class Awerage Arrivals ofer,$],[1,$Mour$],[2,4],[3,4],[4,4],[,2]]$

Six servers process the customers, and each can handle an average of four customers per hour. The service rate is Polsson. Refer to the Tablet $18$ for $L_q$ values.

a$.$ What is the server utilization? $($Round the finol answer to $2$ decimol ploces.$)$

Server utilization

$0\mathrm{.}8$

b$.$ What is the awerage wait time for service by customers in the varlous classes? How many are waiting in each class on average? $($Do not round intermediate colculations. Round the final onswers to $3$ decimal pleces.$)$

$\backslash$table$[[$Closs$,$Average walt t$,,$Length of the,wait$],[1,,$kover,,$],[2,,$hour,,$],[3,,$hour,,$],[4,,$hour,,$]]$

c$.$ II the average arrival rate of the second pricerity class could be reduced to thee customers per hour by shifting some artivals into the thid prionty closs $($which makes its average artwal rate $5$ per hour$)$ how would your answers to part b change? $($Do not round intermediste colculations. Round the final answers to $3$ decimsl pleces.$)$