Scalable Problems and Memory-Bounded Speedup

In this paper three models of parallel speedup are studied. They are fixed-size speedup, fixed-time speedup and memory-bounded speedup. The latter two consider the relationship between speedup and problem scalability. Two sets of speedup formulations are derived for these three models. One set considers uneven workload allocation and communication overhead, and gives more accurate estimation. Another set considers a simplified case and provides a clear picture on the impact of the sequential portion of an application on the possible performance gain from parallel processing. The simplified fixed-size speedup is A mdaM's law. The simplified fixed-time speedup is Gustafson's scaled speedup. The simplified memory-bounded speedup contains both Amdahl's law and Gustafson's scaled speedup as special cases. This study leads to a better understanding of parallel processing. _Research was supported in part by the National Aeronautics and Space Administration under NASA Contract No. NASl-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681. Research was also supported in part by the NSF grant ECS-88-14207. 2Research was supported in part by the NSF grant ECS-88-14207.