Amdahl's law in the era of process variation

Abstract

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%.

The Effect of Temperature on Amdahl Law in 3D Multicore Era

“…Hence, multicore designers should seek ways to reduce the activity of processing cores without decreasing their performance, to enable an efficient 3D integration of a large scale CMPs. Heterogeneous CMP [8] is one possibility. A radically different, non-CMP 3D architecture employing associative processing has also been shown to deliver high performance while maintaining temperatures compatible with 3D DRAM integration [16].…”

“…Wang and Skadron [13] added supply voltage and operating frequency to Hill and Marty performance model. Recently, Ananthanarayanan et al [8] extended Amdahl's law to account for process variations. In this work, we study the thermal effects of 3D integration on performance and scalability of a multicore from Amdahl's law perspective, a subject not addressed by prior research into corollaries of Amdahl's law in multicore era.…”

“…Woo and Lee [4] extended the multicore performance and scalability model by addressing power consumption. Cassidy and Andreou [1] further developed the framework to account for optimal area allocation between core and memory, while Loh [8] extended Hill and Marty's model by adding the cost of the "uncore" resources. Chung et al [5] extended the multicore corollary of Amdahl's law for heterogeneous architectures (including accelerators, such as FPGA, ASIC or GPU in addition to conventional processing cores).…”