Speedup versus efficiency in parallel systems

The tradeoff between speedup and efficiency that is inherent to a software system is investigated. The extent to which this tradeoff is determined by the average parallelism of the software system, as contrasted with other, more detailed, characterizations, is shown. The extent to which both speedup and efficiency can simultaneously be poor is bound: it is shown that for any software system and any number of processors, the sum of the average processor utilization (i.e. efficiency) and the attained fraction of the maximum possible speedup must exceed one. Bounds are given on speedup and efficiency, and on the incremental benefit and cost of allocating additional processors. An explicit formulation, as well as bounds, are given for the location of the knee of the execution time-efficiency profile, where the benefit per unit cost is maximized