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New model for the clustering of errors on telephone circuits (Berger & M 1963)

In: Multifractals and 1/ƒ Noise

Author

Listed:
  • Benoit B. Mandelbrot

    (Yale University, Mathematics Department
    IBM T.J. Watson Research Center)

Abstract

This paper proposes a new mathematical model to describe the occurrence of errors in data transmission on telephone lines. We claim that the distribution of inter-error intervals can be well approximated by a Pareto distribution of exponent less than one. It follows that the relative number of errors and the information-theoretical equivocation tend to zero as the length of the message is increased. The validity of those claims is demonstrated with the aid of experimental data obtained from the German telephone network. Further consequences, refinements, and uses of the model are described.

Suggested Citation

  • Benoit B. Mandelbrot, 1999. "New model for the clustering of errors on telephone circuits (Berger & M 1963)," Springer Books, in: Multifractals and 1/ƒ Noise, chapter 0, pages 132-165, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2150-0_6
    DOI: 10.1007/978-1-4612-2150-0_6
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