Question

I am working on a homework assignment. I seem to be having difficulties applying Amdahl's Law. I feel as if I am working the problem out correct. Here is the question I am working on.

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 learn 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 1.4 times as fast for $5,000.

a. Which would you choose to yield the best performance improvement for the least amount of money?

b. Which option would you choose if you don't care about the money, but want a faster system?

c. What is the break-even point for the upgrades? That is, what price would we need to charge for the CPU (or the disk – change only one) so the result was the same cost per 1% increase for both?

I worked the formula and received the same amount of money for the 1% improvement. For the disk option i did, f=.4, k=2.5. When I plugged these numbers into the formula i got a speedup of 32%. For the CPU option, f=.6, k=1.4. I got a speed up of 20%. But the cost per 1% improvement, I am getting the same number of $250. Is my math off somewhere?

Was it helpful?

Solution

I wonder if perhaps this is simply a rounding error?

SU(Disk) = 1.31579

http://wolfr.am/102zBzb

SU(CPU) = 1.2069

http://wolfr.am/102zxiL

So I see where you got 32% and 20%, but you have rounded-up to get 32%, and rounded-down to get 20%. You'll notice if you try 32% and 21%, you get a different cost per 1% speed-up

Personally, I would probably use 31.6 and 20.7 (or even the full 31.579 and 20.69).

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