To calculate speed up performance various laws have been developed. These laws are discussed here.
Remember, the speed up factor helps us in knowing the relative gain achieved in shifting the implementation of a task from sequential computer to parallel computer and the performance does not enhance linearly with the increase in number of processors. Due to the above reason of saturation in 1967 Amdahl's law was derived. Amdahl's law states that a program have two types of operations i.e. complete sequential operations which should be done sequentially and complete parallel operations which can be implemented on multiple processors. The statement of Amdahl's law can be described with the help of an example.
Let us take a problem say P which has to be solved using a parallel computer. According to Amdahl's law, there are generally two types of operations. Thus, the problem will have some sequential operations and some parallel operations. We already know that it needs T (1) amount of time to implement a problem using a sequential algorithm and sequential machine. The time to compute the sequential operation is a fraction α (alpha) (α ≤ 1) of the total implementation time i.e. T (1) and the time to compute the parallel operations is (1- α). Thus, S (N) can be calculated as under: