On parallel processing systems: Amdahl´s law generalized and some results on optimal design

The authors model a job in a parallel processing system as a sequence of stages, each of which requires a certain integral number of processors for a certain interval of time. They derive the speedup of the system for two cases: systems with no arrivals, and systems with arrivals. In the case with no arrivals, their speedup result is a generalization of Amdahl´s law (G.M. Amdahl, 1967). They extend the notion of power as previously applied to general queuing and computer-communication systems to their case of parallel processing systems. They find the optimal job input and the optimal number of processors to use so that power is maximized. Many of the results for the case of arrivals are the same as for the case of no arrivals. It is found that the average number of jobs in the system with arrivals equals unity when power is maximized. They also model a job in such a way that the number of processors required continuously varies over time. The same performance indices and parameters studied in the discrete model are evaluated for this continuous model