Problem $18-14($Algo$)$

Customers arriving at a service center are assigned to one of three categories, with category $1$ given the highest priority. Records

indicate that an average of $8\mathrm{.}0$ customers arrive per hour and that one$-$third are assigned to each category. There are two servers, and

each can process customers at the rate of $5\mathrm{.}0$ per hour. Arrival and service rates can be described by Poisson distributions. Use Table

$18\mathrm{.}4.$

a$.$ What is the utilization rate for this system? $($Round your answer to $2$ decimal places.$)$

$$

b$.$ Determine the average waiting time for units in each class. $($Round your intermediate calculations and final answers to $2$ decimal

places.$)$

c$.$ Find the average number of customers in each class that are waiting for service. $($Round your intermediate calculations and final

answers to $2$ decimal places.$)$Customers arriving at a service center are assigned to one of three categories, with category $1$ given the highest priority. Records indicate that an average of $8\mathrm{.}0$ customers arrive per hour and that one$-$third are assigned to each category. There are two servers, and each can process customers at the rate of $5\mathrm{.}0$ per hour. Arrival and service rates can be described by Poisson distributions. Use Table $18\mathrm{.}4.$

a$.$ What is the utilization rate for this system? $($Round your answer to $2$ decimal places.$)$

b$.$ Determine the average waiting time for units in each class. $($Round your intermediate calculations and final answers to $2$ decimal places.$)$

c$.$ Find the average number of customers in each class that are waiting for service. $($Round your intermediate calculations and final answers to $2$ decimal places.$)$