Article: Amdahl's law in the era of process variation Journal: International Journal of High Performance Systems Architecture (IJHPSA) 2013 Vol.4 No.4 pp.218 - 230 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%. Inderscience Publishers - linking academia, business and industry through research

Title: Amdahl's law in the era of process variation

Authors: Gayathri Ananthanarayanan; Geetika Malhotra; M. Balakrishnan; Smruti R. Sarangi

Addresses: School of Information Technology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India ' Computer Science and Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India ' Computer Science and Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India ' Computer Science and Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India

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%.

Keywords: process variation; Amdahl's law; equivalent core; multicore modelling; multicore processors; Monte Carlo simulation; advanced scheduling.

DOI: 10.1504/IJHPSA.2013.058984

International Journal of High Performance Systems Architecture, 2013 Vol.4 No.4, pp.218 - 230

Received: 10 Dec 2012
Accepted: 28 Aug 2013
Published online: 25 Jul 2014 *

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Title: Amdahl's law in the era of process variation

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