Multiprocessor speed-up, Amdahl's Law, and the Activity Set Model of parallel program behavior

An important issue in the effective use of parallel processing is the estimation of the speed-up one may expect as a function of the number of processors used. Amdahl's Law has traditionally provided a guideline to this issue, although it appears excessively pessimistic in the light of recent experimental results. In this note, Amdahl's Law is amended by giving a greater importance to the capacity of a program to make effective use of parallel processing, but also recognizing the fact that imbalance of the workload of each processor is bound to occur. An activity set model of parallel program behavior is then introduced along with the corresponding parallelism index of a program, leading to upper and lower bounds to the speed-up.