Question

Amdahl’s LAW Question:

Suppose that we want to enhance the execution time used for web serving, two designs have been proposed, show which one is better
Design 1: Use a new processor 15 times faster than the original processor, assuming that the original processor is busy with computation 50% of the time and waiting for the I/O 50% of the time.
Design 2: Use a new Processor 20 time faster. While the processor is 30% of the time busy with the computation and 70% waiting for the IO

Answer 1

Step-by-step explanation:

As per Amdahl's law :

`\text {Speedup} = {\frac{\text{Old Execution time}}{\text {New Execution time} }`

`\text {Speedup} = \frac{1}{( (1- \text {FractionEnhanced}) + (\text {FractionEnhanced} / \text {SpeedupEnhanced}) )}`

Here :

Design 1:

FractionEnhanced = 0.5 (50% of computation )

[ Note that I/O wait has nothing to do with speed ]

SpeedupEnhanced = 15 times

`\text {Overall speedup} =(1)/(( ( 1- 0.5) + (0.5/ 15) ))`

`\text {overall Speedup} = (1)/((0.5 + 0.033))`

`\text {overall Speedup} = (1)/( 0.533) = 1.876`

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Design 2:

FractionEnhanced = 0.3 (30% of computation )

SpeedupEnhanced = 20 times

`\text {overall speedup} = 1 / ( ( 1- 0.3) + (0.3/ 20) )\\\\\text {overall speedup} = 1/ (0.7 + 0.015)\\\\\text {overall speedup} = 1/ 0.715 \\\\\text {overall speedup}= 1.398`

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So as we can see Design 1 is better with overall speedup of 1.876 times the original processor.