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Implications

The following is a quote from Gene Amdahl, in 1967:

"For over a decade prophets have voiced the contention that the organization of a single computer has reached its limits and that truly significantly advances can be made only by interconnection of a multiplicity of computers in such a manner as to permit cooperative solution... The nature of this overhead (in parallelism) appears to be sequential so that it is unlikely to be amenable to parallel processing techniques. Overhead alone would then place an upper limit on throughput of five to seven times the sequential processing rate, even if the housekeeping were done in a separate processor... At any point in time it is difficult to foresee how the previous bottlenecks in a sequential computer will be effectively overcome."

Through the quote, Amdahl indicated that whatever concurrent and parallel techniques are implemented in a program, the sequential nature of the overhead portion required in the program always sets an upper boundary on how much speedup the program will gain. This is one of the implications that Amdahl's Law further suggests. Consider the following example:

denotes the speedup gained from n processors

This shows that, as the number of resources (specifically, the number of available processors) increases, the speedup of the execution of the whole task also increases. However, this does not mean that we should always implement concurrency and parallelism with as many system processors as possible, to achieve the highest performance. In fact, from the formula, we can also gather that the speedup achieved from incrementing the number of processors decreases. In other words, as we add more processors for our concurrent program, we will obtain less and less improvement in execution time.

Furthermore, as mentioned previously, another implication that Amdahl's Law suggests concerns the upper limit of the execution time improvement:

is the cap of how much improvement concurrency and parallelism can offer your program. This is to say that, no matter how many available resources your system has, it is impossible to obtain a speedup larger than through concurrency, and this limit is dictated by the sequential overhead portion of the program (B is the fraction of the program that is strictly serial).