Amdahl's law in the era of process variation

In this paper we propose to extend Amdahl's law for modelling multicores with process variation using simple mathematical techniques. We consider three major families of multicore processors - symmetric, asymmetric, and dynamic. We consider a conservative operating mode for setting the target frequency plain, and a more optimised method opt. Subsequently, we propose three separate corollaries to the standard Amdahl's law to model the performance of different multicore configurations with different modes of operation. We observe that most of the major trends published in prior work or the ones that we observe through Monte Carlo simulations can be explained by a simple hypothetical concept called an equivalent core. The crux of our approach is to look at a set of equivalent cores with no variation that have the same performance as the target system. It is much simpler and much more intuitive to reason in terms of equivalent cores. Along with being an effective analytical tool, it can be used to speed up a lot of heuristics, and can be exposed to higher level software for advanced scheduling decisions. Lastly, we validate our models with experiments on a real system, and the maximum error is limited to 8%.