Speedup for multi-level parallel computing

This paper studies the speedup for multi-level parallel computing. Two models of parallel speedup are considered, namely, fixed-size speedup and fixed-time speedup. Based on these two models, we start with the speedup formulation that takes into account uneven allocation and communication latency, and gives an accurate estimation. Next, we propose a high-level abstract case with providing a global view of possible performance enhancement, namely E-Amdahl's Law for fixed-size speedup and E-Gustafson's Law for fixed-time speedup. These two laws demonstrate seemingly opposing views about the speedup of multi-level parallel computing. Our study illustrates that they are not contradictory but unified and complementary. The results lead to a better understanding in the performance and scalability of multi-level parallel computing. The experimental results show that E-Amdahl's Law can be applied as a prediction model as well as a guide for the performance optimization in multi-level parallel computing