A Model of the Switched Telephone Network for Data Communications

In the study of errors on data communication channels, several mathematical models of the error process have been proposed. Gilbert1 proposed a two-state Markov process, and Berger and Mandelbrot2 have employed a Pareto distribution to fit data collected from the German telephone network. Sussman3 has applied a Pareto fitting to part of the Alexander-Gryb-Nast data.4 Common to the models of Gilbert and Berger-Mandelbrot is the assumption that the error process is of the renewal type wherein the state of a bit-error is the renewal event whose occurrence frees the process from dependence upon past history and starts it anew. In such models the distributions of lengths of error-free intervals (gaps) determine the processes, because the lengths of the gaps before and after an error are independently distributed. One may calculate from this distribution the probabilities P(m,n) that m bit-errors occur in a block of n consecutive bits. These probabilities are useful 89 90 T H E B E L L SYSTEM TECHNICAL JOURNAL, JANUARY 1965