A Statistical Analysis of Telephone Circuit Error Data

Berger and Mandelbrot in 1963 proposed a particular renewal process as a model for the occurrence of errors in data transmitted over telephone circuits. Besides the assumed independence between the successive intervals between errors, they assume that the intervals have a Pareto distribution. Their graphical analyses of large amounts of data indicated departures from the model which Mandelbrot proposed in 1964 to account for in an extended model. Some simple formal statistical procedures are given for analyzing this sort of data, procedures that are not affected by the possibility that the population mean-interval-between-errors is infinite. The departures from independence of intervals noted by Berger and Mandelbrot are formally verified from the analysis of data from a single data transmission test. A separate analysis of another set of data is also made and the results are compared to see what features of the error patterns are general, and what features are particular to different transmission conditions. In both sets of data analyzed, the outstanding feature detected is the strong positive correlation between successive long intervals between errors. Evidence is also found which indicates that the upper tail of the marginal distribution of intervals between errors does not follow a hyperbolic law.