Power-Law Distributions in Hard Drive Behavior

Dominik Strzałka, Piotr Szurlej

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DOI: 10.4236/jsea.2011.412083                

Abstract

Taking into account the fact that the computer systems, as the implementations of Turing machine, are physical devices, the paper shows considerations in which hard drive behavior will be presented in terms of statistical mechanics. Because computer is a machine, its analysis cannot be based only on mathematical models apart of physical conditions. In the paper it will be presented a very narrow part this problem – an analysis of hard drive behavior in the context of the power-law distributions. We will focus only on four selected hard drive parameters, i.e. the rate of transfer bytes to or from the disk during the read or write, the number of pending requests to the disk and the rate of read operations. Our research was performed under the Windows operating system and this allows to make a statistical analysis for the possible occurrence of power-laws representing the lack of characteristic scale for considered processes. This property will be confirmed in all analyzed cases. A presented study can help describing the behavior of the whole computer system in terms of physics of computer processing.

Keywords

Power Laws, Hard Drive Behavior, Performance Monitor, Windows Operating System, Physics of Computer Processing

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. Descartes, “Discourse on Method and Meditations,” The Liberal Arts Press, New York, 1637.
[2]	F. Grabowski and D. Strzalka, “Dynamic Behavior of Simple Insertion Sort Algorithm,” Fundamenta Informaticae, Vol. 72, No. 1-3, 2006, pp. 155-165.
[3]	Y. Bar-Yam, “Dynamics of Complex Systems,” Westview Press, Colorado, 1997.
[4]	M. M Waldrop, “Complexity: The Emerging Science at the Edge of Order and Chaos,” Simon & Schuster, New York, 1997.
[5]	F. Grabowski and D. Strzalka, “Simple, Complicated and Complex Systems—The Brief Introduction,” 2008 Conference on Human System Interactions, Vol. 1-2, 2008, pp. 576-579. doi:10.1109/HSI.2008.4581503
[6]	Aristotle, “Methaphysics,” Clarendon Press, Oxford, 1924.
[7]	P. Wegner, “Research Paradigms in Computer Science,” Proceedings of the 2nd International Conference on Software Engineering, San Francisco, 13-15 October 1976, pp. 322-330.
[8]	D. Strzalka, “Non-Extensive Statistical Mechanics—A Possible Basis for Modeling Processes in Computer Memory System,” Acta Physica Polonica A, Vol. 117, No. 4, 2010, pp. 652-657.
[9]	B. B. Mandelbrot, “How Long Is the Coast of Britain,” Science, Vol. 156, No. 3775, 1967, pp. 636-638. doi:10.1126/science.156.3775.636
[10]	H.-O. Peitgen, H. Jurgens and D. Saupe, “Chaos and Fractals. New Frontiers of Science,” Heidelberg, Springer-Verlag, New York, 1991.
[11]	X. Gabaix, P. Gopikrishnan, V. Plerou and H. E. Stanley, “A Theory of Power-Law Distributions in Financial Market Fluctuations,” Nature, Vol. 423, 2003, pp. 267-270. doi:10.1038/nature01624
[12]	L. A. Adamic and A. B. Huberman, “Power-Law Distribution of the World Wide Web,” Science, Vol. 287, No. 5461, 2000, pp. 2115-2115. doi:10.1126/science.287.5461.2115a
[13]	M. Faloutsos, P. Faloutsos and C. Faloutsos, “On Power-Law Relationships of the Internet Topology,” Proceedings of the Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, Stockholm, 30 August -3 September 1999, pp. 251-262. doi:10.1145/316194.316229
[14]	K. Sharma and S. Sharma, “Power Law and Tsallis Entropy: Network Traffic and Applications,” Chaos, Non-linearity, Complexity Studies in Fuzziness and Soft Computing, Vol. 206, 2006, pp. 162-178. doi:10.1007/3-540-31757-0_5
[15]	Karmeshu and S. Sharma, “Queue Length Distribution of K. Network Packet Traffic: Tsallis Entropy Maximization with Fractional Moments,” IEEE Communication Letters, Vol. 10, No. 1, 2006, p. 34. doi:/10.1109/LCOMM.2006.1576561
[16]	A. Clauset, C. R. Shalizi and M. E. Newman, “Power-Law Distributions in Empirical Data,” SIAM Review, Vol. 51, 2009, pp. 661-703. doi:10.1137/070710111
[17]	H. Bauke, 2007, “Parameter Estimation for Power-Law Distributions by Maximum Likelihood Methods,” The European Physical Journal B, Vol. 58, No. 2, pp. 167-173. doi:10.1140/epjb/e2007-00219-y