Deening and Measuring Scalability

The concept of scalability in parallel systems is a simple one: given a reasonable performance on a sample problem, a problem of increased workload can be solved with reasonable performance given a commensurate increase in computational resources. This definition does not aaord the analytical precision that is required of any scientiic classiication system since the terms of this deenition are almost entirely subjective. Some attempts have been made to measure scalability, but many of the popular measurements do not eliminate subjective terms. For example: the xed-time measurements that have been advanced do not specify a xed-time constraint, and the scaled-speedup measurements do not specify initial workload. The problem with these measurements is that they depend on a subjective deenition of \reasonable performance" and as a result are unreliable. An alternate deenition of scalability can be found when scalability is deened as the ability to maintain cost eeectiveness as workload grows. When this approach is considered, the subjective \reasonable perfor-mance" becomes replaced by an objective term of optimal cost eeectiveness. Obviously the success of this approach depends highly on determining a cost eeec-tiveness function that is relevant to scalability. This paper will introduce a cost eeectiveness function and argue that the proposed cost eeectiveness function is highly relevant to the goals of developing scalable systems .