Amdahl定律与几何Scalability的新解释
A New Interpretation of Amdahl's Law and Geometric Scalability
摘要：
多处理器效应是指由于处理开销而导致的计算周期损失。Amdahl定律和多处理因子（MPF）是工业界和学术界使用的两种缩放模型，用于估计存在这种多处理器效应的多处理器容量。这两种模型表达了不同的收益递减规律。Amdahl定律确定工作负载中具有固定串行化程度的处理器容量递减，而MPF模型将其视为恒定的几何比例。这两个模型的效用性能评估源于存在一个单一的参数，可以很容易地确定从一个小的基准测量。然而，这一效用被一个两难的问题所破坏。这两种模型产生不同的结果，特别是对于当今应用程序非常重要的大型处理器配置。问题自然出现了：这两个模型中哪一个是正确的使用？忽略这个问题只会将容量预测简化为任意曲线拟合。要解决这个难题，需要对这些尺度模型进行动力学解释。我们提出了一个物理解释的基础上排队论和Amdahl的法律对应于同步排队的总线模型，而MPF模型属于Coxian服务器模型。后者表现出非物理效应，如次线性响应时间，因此，我们警告它的使用大型多处理器配置。
英文摘要：
The multiprocessor effect refers to the loss of computing cycles due to processing overhead. Amdahl's law and the Multiprocessing Factor (MPF) are two scaling models used in industry and academia for estimating multiprocessor capacity in the presence of this multiprocessor effect. Both models express different laws of diminishing returns. Amdahl's law identifies diminishing processor capacity with a fixed degree of serialization in the workload, while the MPF model treats it as a constant geometric ratio. The utility of both models for performance evaluation stems from the presence of a single parameter that can be determined easily from a small set of benchmark measurements. This utility, however, is marred by a dilemma. The two models produce different results, especially for large processor configurations that are so important for today's applications. The question naturally arises: Which of these two models is the correct one to use? Ignoring this question merely reduces capacity prediction to arbitrary curve-fitting. Removing the dilemma requires a dynamical interpretation of these scaling models. We present a physical interpretation based on queueing theory and show that Amdahl's law corresponds to synchronous queueing in a bus model while the MPF model belongs to a Coxian server model. The latter exhibits unphysical effects such as sublinear response times hence, we caution against its use for large multiprocessor configurations.
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