Implications

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

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).