Accounting Start-up Time of Parallel Processes in Amdahl's Law

Abstract

The conventional form of Amdahl’s law states that speedup of calculations in a multiprocessor machine is limited by the definite constant value just due to the existence of some non-parallelizable part in any algorithm. This brief paper considers one more general reason, which prevents a growth of parallel performance: processes that implement distributed task cannot start simultaneously and hence every process adds some start-up time, also reducing by that the gain from a parallel processing. The simple formula, proposed here to extend Amdahl’s law, leads to a less optimistic picture in comparison with classical results: for large amount of processor units the modified law does not approach to constant but vanishes. This is the result of competition between two factors: decreasing of calculation duty and increasing of start-up time when a number of parallel processes grows. The effect may be subdued by means of specific regularity in launching parallel processes.