$7.$ CPU$-$on$-$Demand $($CPUD$)$ offers real$-$time high$-$performance computing services. CPUD

owns one supercomputer that can be accessed through the Internet. Its customers

send jobs that arrive, on average, every five hours. The standard deviation of the

interarrival times is five hours. Executing each job takes, on average, three hours on

the supercomputer and the standard deviation of the processing time is $4\mathrm{.}5$ hours.

What is the utilization $($as a percent$)$ of CPUD$$s supercomputer?

Problems and Applications

LO$16-1$

$1.$ The Shady Farm Milk Company can process milk at a fixed rate of $7500$ gallons$/$hour$.$

The company$$s clients request $100,000$ gallons of milk over the course of one day. This

demand is spread out uniformly from $8$ a$.$m$.$ to $6$ p$.$m$.$ The company starts producing at

$8$ a$.$m$.$ and continues to work until all of the demand has been satisfied. At noon, how

many gallons of milk are in the queue to be processed?

$2.$ Using the previous question, change the fixed rate that milk is processed to $6000$ gallons$/$hour; all the other factors remain the same. How long does the client requesting

milk at $6$ p$.$m$.$ have to wait to have its demand satisfied $($in hours$)?$

$3.$ Using question $1,$ change the fixed rate that milk is processed to $5000$ gallons$/$hour; all

the other factors remain the same. On average, how long does a client wait $($in hours$)$ to

receive its product?

LO$16-2$

$4.$ Which of the following lines in the graphs in Figure $16\mathrm{.}16$ best depicts the relationship

between utilization and waiting time in a queuing system? $($Assume the utilizations

depicted are less than $100$ percent.$)$

Figure $16\mathrm{.}16$

Waiting Time

Utilization

D

E

F

Waiting Time

Utilization

A

B

C

Final PDF to printer

cac$42205\_$ch$16\_528-570.$indd $56712/28/1507$:$55$ PM

Chapter Sixteen Service Systems with Patient Customers $567$

$8.$ Using the information in the previous question, how long does a customer have to wait

to have a job completed?