Terminology

Amdahl's Law provides a mathematical formula that calculates the potential improvement in speed of a concurrent program by increasing its resources (specifically, the number of available processors). Before we can get into the theory behind Amdahl's Law, first, we must clarify some terminology, as follows:

• Amdahl's Law solely discusses the potential speedup in latency resulting from executing a task in parallel. While concurrency is not directly discussed here, the results from Amdahl's Law concerning parallelism will nonetheless give us an estimation regarding concurrent programs.
• The speed of a program denotes the time it takes for the program to execute in full. This can be measured in any increment of time.
• Speedup is the time that measures the benefit of executing a computation in parallel. It is defined as the time it takes a program to execute in serial (with one processor), divided by the time it takes to execute in parallel (with multiple processors). The formula for speedup is as follows:

In the preceding formula, T(j) is the time it takes to execute the program when using j processors.