The Placing of Multiplexers to Minimise Cable Distance

Abstract

We wish to site a given number of multiplexers, used in communication networks to cut cable costs, so that the main cable distance between a terminal and its nearest multiplexer and between the multiplexer and its nearest computer is a minimum. It is shown that the density of the multiplexer should be proportional to the two-thirds power of the terminal density and that the computer density should be directly proportional to the multiplexer density. An illustration is given of how this theoretical result can be used to minimise cable costs for the case of a communications network serving a single computer.