Implications of Merging Phases on Scalability of Multi-core Architectures

Amdahl\u27s Law dictates that in parallel applications serial sections establish an upper limit on the scalability. Asymmetric chip multiprocessors with a large core in addition to several small cores have been advocated for recently as a promising design paradigm because the large core can accelerate the execution of serial sections and hence mitigate the scalability bottlenecks due to large serial sections. This paper studies the scalability of a set of data mining workloads that have negligible serial sections. The formulation of Amdahl\u27s Law, that optimistically assumes constant serial sections, estimates these workloads to scale to hundreds of cores in a chip multiprocessor (CMP). However the overhead in carrying out merging (or reduction) operations makes scalability to peak at lesser number. We establish this by extending the Amdahl\u27s speedup model to factor in the impact of reduction operations on the speedup of applications on symmetric as well as asymmetric CMP designs. Our analytical model estimates that asymmetric CMPs with one large and many tiny cores are only optimal for applications with a low reduction overhead. However, as the overhead starts to increase, the balance is shifted towards using fewer but more capable cores. This eventually limits the performance advantage of asymmetric over symmetric CMPs