Question

Suppose we could improve the speed of the CPU in a computer by a factor of 5 (without affecting I/O performance) for 5 times the cost. Also assume that the CPU is used 50% of the time, and the rest of the time the CPU is waiting for I/O. If the CPU is one-third of the total cost of the computer, is increasing the CPU speed by a factor of 5 a good investment from a cost/performance viewpoint?

Answer 1

Answer:

Bad Investment

Explanation:

• Fraction enhanced = 50% = 0.5 (50% CPU is used all times and rest is waiting for I/O.
• Speed up = 5 (By a factor of CPU speed is increased)

• Speed up (overall) = $\frac{1}{1-Fraction enhanced + \frac{Fraction enhanced}{Speedup enhanced} }$

• Speed up (overall) = $\frac{1}{(1-0.5)+\frac{0.5}{5} } = 1.67$

• CPU = 1/3rd the total cost which means rest of the 2/3rd cost remains the same.
• New cost of machines = (2/3 * 1) + (1/3 * 5) = 2.33
• This means new machine is 2.33 times the cost of the old machine.

• $\frac{Cost increase}{Performance increase} = \frac{2.33}{1.67} = 1.3980$

• As seen above cost increase is greater then performance increase therefore this is a BAD Investment.