Question

Suppose your company has decided that it needs to make certain busy servers faster. Processes in the workload spend 60% of their time using the CPU and 40% on I/O. To achieve an overall system speedup of 25%: a. How much faster does the CPU need to be? b. How much faster does the disk need to be?

Answer 1

Answer:

CPU need 50% much faster

disk need 100% much faster

Explanation:

given data

workload spend time CPU  = 60%

workload spend time I/O = 40%

achieve overall system speedup = 25%

to find out

How much faster does CPU need and How much faster does the disk need

solution

we apply here Amdahl’s law for the overall speed of a computer that is express as

S = $\frac{1}{(1-f)+ \frac{f}{k} }$      .............................1

here f is fraction of work i.e 0.6 and S is overall speed  i.e 100% + 25% = 125 % and k is speed up of component

so put all value in equation 1 we get

S = $\frac{1}{(1-f)+ \frac{f}{k} }$  

1.25 = $\frac{1}{(1-0.6)+ \frac{0.6}{k} }$  

solve we get

k = 1.5

so we can say  CPU need 50% much faster

and

when f = 0.4 and S = 125 %

put the value in equation 1

S = $\frac{1}{(1-f)+ \frac{f}{k} }$  

1.25 = $\frac{1}{(1-0.4)+ \frac{0.4}{k} }$  

solve we get

k = 2

so here disk need 100% much faster