A New Model for Error Clustering in Telephone Circuits

This paper proposes a new mathematical model to describe the distribution of the occurrence of errors in data transmission on telephone lines. We suggest: a) that the statistics of telephone errors can be described in terms of an error probability depending solely on the time elapsed since the last occurrence of an error; b) that the distribution of inter-error intervals can be well approximated by a law of Pareto of exponent less than one; the relative number of errors and the equivocation tend, therefore, to zero as the length of the message is increased. The validity of those concepts is demonstrated with the aid of experimental data obtained from the German telephone network. Further consequences, refinements, and uses of the model are described in the body of the paper.