Question

1. Suppose the daytime processing load consists of 60% CPU activity and 40% disk activity. Your customers are complaining that the system is slow. After doing some research, you have learned that you can upgrade your disks for $8,000 to make them 2.5 times as fast as they are currently. You have also learned that you can upgrade your CPU to make it 1.5 times as fast as the current CPU for $5,000.

a. Which upgrade option would give a faster system?

b. Which upgrade option would give the best return of investment for each percent of speed improvement?

Show your calculation to support your conclusion.

2. Suppose a disk drive has the following characteristics:

• 6 surfaces

• 1024 tracks per surface

• 256 sectors per track

• 512 bytes/sector

• Track-to-track seek time of 8 milliseconds

• Rotational speed of 5000 RPM.

a. What is the total capacity of the drive?

b. What is its average access time?

Answer 1

1)

SpeeedUp can be calculated using Amadahl's Law

SpeedUp achieved by upgrading disks is

$SpeedUp=\frac{1}{(1-0.4) +\frac{.4}{2.5}}=\frac{1}{0.76}=1.31$

SpeedUp achieved by upgrading CPU is

$SpeedUp=\frac{1}{(1-0.6) +\frac{.6}{1.5}}=\frac{1}{0.8}=1.25$

a) So upgrading Disks gives a faster system as the speedup is more.

b) SpeedUp increase in case of disk is 31% and in case of CPU is 25%

Investment for speed increase for each percent in case of disk = $8000 / 31 = $258

Investment for speed increase for each percent in case of CPU = $5000 / 25 = $200

So increasing CPU speed is a better option

2)

a)

Total Capacity of the drive = Surfaces x tracks per surface x  sectors per track x  bytes/sector

Total Capacity of the drive = 6 x 1024 x 256 x 512 = 8589934592 bytes = 8 GB

b)

Average seek time = (Sum of all possible seek times)/(Total no. of possible seek times)

But in practice it is determined by statistical methods or simply approximated as the time of a seek over one-third of the number of tracks

So average seek time is 48 / 3 = 16 ms

Average rotational Latency is half of the time required to complete 1 rotation

Average latency = 0.5*Latency Time

Average latency = 0.5 * 0.2 = 0.1 ms

average access time = Average seek time + Average latency = 16 ms + 0.1ms = 16.1 ms