한국정보과학회논문지:시스템및이론 (Journal of KIISE:Computer Systems and Theory)

한국정보과학회 (Korean Institute of Information Scientists and Engineers)
권호 표지

다중 프로세서에서의 캐시접근 실패율을 위한 경험적 모델링

Empirical Modeling for Cache Miss Rates in Multiprocessors

  • 이강우 (동국대학교 정보통신공학과) ;
  • 양기주 (동국대학교 정보통신공학과) ;
  • 박춘식 (동국대학교 정보통신공학과)
  • 발행 : 2006.02.01
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⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는, 소규모 시뮬레이션을 통하여 수집된 표본에 통계적인 추정방법을 적용하여 모델을 구하는 경험적 모델링 기법을 제안한다. 이 기법을 이용하여 대칭형 구조를 갖는 다중프로세서 시스템에서의 캐시접근실패율을 위한 두 종류의 모델을 구하였다. 목표시스템의 사양이 고정되었을 때 입력데이타의 크기변화에 따르는 모델과, 입력데이타의 크기가 고정되었을 때 목표시스템의 프로세서 수의 변화에 따르는 모델이다. 모델의 정확성을 제고하기 위하여 한 프로그램에 존재하는 공유데이타들에 대하여 종류별 캐시접근실패에 대한 개별적인 모델들을 구한 후 이들을 종합함으로써 최종적인 모델을 구하였다. 또한 최소 제곱 추정법과 로버스트 추정법을 병용하여 이탈점으로 인한 왜곡을 최소화함으로써 모델의 정확도를 향상시켰다. 경험적 모델링은 표본에 대한 분석이 필요 없으면서도 모델의 정확도가 매우 높다. 또한 소규모의 시뮬레이션만 수행하면 되고, 실험을 통하여 일련의 표본을 수집할 수만 있으면 모든 분야의 연구에 적용할 수 있다. 경험적 모델을 이용한 24가지 경우의 예측시도 중 17번의 경우에는 $1\%$ 미만의 예측오차율을 보였으며, 나머지 경우에도 매우 높은 정확도를 보였다. 특히 프로그램의 실행양식이 불규칙하거나, 표본의 수가 충분하기에는 부족한 경우에도 좋은 결과를 보여준다.

This paper introduces an empirical modeling technique. This technique uses a set of sample results which are collected from a few small scale simulations. Empirical models are developed by applying a couple of statistical estimation techniques to these samples. We built two types of models for cache miss rates in Symmetric Multiprocessor systems. One is for the changes of input data set size while the specification of target system is fixed. The other is for the changes of the number of processors in target system while the input data set size is fixed. To develop accurate models, we built individual model for every kind of cache misses for each shared data structure in a program. The final model is then obtained by integrating them. Besides, combined use of Least Mean Squares and Robust Estimations enhances the quality of models by minimizing the distortion due to outliers. Empirical modeling technique produces extremely accurate models without analysis on sample data. In addition, since only snail scale simulations are necessary, once a set of samples can be collected, empirical method can be adopted in any research areas. In 17 cases among 24 trials, empirical models present extremely low prediction errors below $1\%$. In the remaining cases, the accuracy is excellent, as well. The models sustain high quality even when the behavioral characteristics of programs are irregular and the number of samples are barely enough.

키워드

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