International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Rakitskiy A.   Ryabko B.Y.  

An information-theoretic approach to estimation of the capacity of computers and supercomputers

Reporter: Ryabko B.Y.

An information-theoretic approach to estimation of  the capacity of computers and supercomputers

B.  Ryabko1,2* ,  A. Rakitskiy3,1

1Institute of Computational Technologies of SB RAS, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
3Siberian State University of Telecommunications and Informatics,  Novosibirsk, Russia
*e-mail address:

Currently, there are many approaches to evaluate the performance of computer systems. Basically most of the methods is
the use of benchmarks, i.e. a test set
of tasks, which helps to determine execution time required  to solve
them. Comparison of computers is performed on the analysis
of these execution times.
A disadvantage of benchmarks is the need to have
a working model of tested system. This imposes restrictions
on the usage and increases the cost of the evaluation and
comparison of computers. Besides, it is impossible to use benchmarks
in order to evaluate computer during the development phase,
when there is no working model. Moreover, the objectiveness
of benchmarks is reduced by the fact that they are focused on
specific tasks.
A concept of computer capacity was suggested in [1,2] and then it was applied to analysis of computers of different kinds, see [3-5]. The computer capacity characterizes  the
performance of real computers with different  CPU clock speed, number of processor cores, memory
organization and instruction set of processors, etc. It is important to note that the computer capacity is estimated theoretically based on  instruction set of processors and their execution times, including latencies of accessing
to different types of memory (cache-memory, RAM, etc.), as well as delays associated to restarting the pipeline, to changing of processor context and with exceptions that occur during the execution of instructions. Note that the basis of the developed approach is the concept of Shannon entropy, capacity of the discrete channel   and some other ideas, which included in Informational Theory.
In this report we apply the computer capacity for analysis of modern supercomputers. More precisely, we estimate the computer capacity for three following  CRAY      supercomputers from the top 500 list (November, 2015): Trinity - Cray XC40 (, Hazel Hen - Cray XC40 (, and Shaheen II - Cray XC40 (, which are the sixth, eighth and ninth in the list, see .  It turned out that our theoretical estimations are close to ones derived from benchmarks.  Also we consider how the supercomputer parameters  have an influence on the capacity and make some recommendations how to increase the performance.

[1] B. Ryabko, “An information-theoretic approach to estimate the capacity of processing units” , Performance Evaluation, 69, pp. 267-273 (2012).
[2] B. Ryabko, “On the efficiency and capacity of computers”,  Applied Mathematics Letters, 25 , pp. 398 – 400 (2012).
[3]  A. Rakitskiy, B. Ryabko,  A. Fionov,  “Evaluation of Computer Capacity for P5 Intel
Processors”,  In: XIII symposium on problems of redundancy in  information and control systems, pp. 70-73 (2012).
[4] B. Ryabko, A. Fionov,  “Estimating the performance of computer systems through computer capacity”. In: XIII symposium on problems of redundancy in  information and control systems,  pp. 74 - 77  (2012).
[5] A. Fionov., Y.  Polyakov, B. Ryabko,  “'Application of computer capacity to evaluation of intel x86 processors”,  Advances in Intelligent and Soft Computing, AISC, 145, pp.99-104, (2012).

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