The computer sends 82 of the time computing and 18 waiting f

The computer sends 82% of the time computing and 18% waiting for the disk. The instruction mix and the average cycles per instruction (CPI) for each type is:

Type

Instruction %

CPI

Int

40 %

1

FP

30 %

5

Other

30 %

2

A) Consider 3 modifications to the computer. Compute the speedup for each. Then show which modification gave the best speedup?

            I. The processor is replaced with a new one that reduces the total computation time by 35%.

           II. The disk is replaced with a solid state device that reduces the disk waiting time by 85%.

           III. The processor is replaced with a new one that has improved floating point performance. The average floating point CPI is reduced to 3; all other aspects are unchanged.

Solution

CPI means Cycles per Instructions

Speedup is a metric for relative performance improvement when executing a task. The notion of speedup was established by Amdahl\'s law, which was particularly focused in the context of parallel processing.

Given 82% of the time computing and 18% waiting for the disk

When the processor is replaced with a new one that reduces computation time by 35%

Speedup = 1 / ((1-0.82)+ 0.82 *0.65)

                 = 1/(0.18+0.82*0.65)

                =1 /(0.18+0.533) = 1/0.713 = 1.4025254 = 1.40

If the disk is replaced by a solid state that reduces the disk waiting time by 85%

Speedup is = 1/ ((1.0-0.18) +0.18*0.15)

                    = 1/(0.82+0.18*0.15)

                   = 1/0.847

                    =1.180637544 = 1.18

Before modification of the system CPI for the given is:

=0.40*1+0.30*5+0.30*2 = 0.40+1.50+0.60 = 2.50

CPI after the changing = 0.40*1+0.30*3+0.30*2

                                            =0.40+0.90+0.60 = 1.90

To computation Speedup = before changing CPI / After changing CPI = 2.5/1.9 = 1.315789

Speedup = 1/((1-0.82)+0.82/1.315789) = 1/(0.18+0.62320) = 1/0.803200 = 1.2450199