THE ANALYTICAL FORM OF THE LENGTH DISTRIBUTION FUNCTION FOR COMPUTER INTERCONNECTIONS

With the ever-increasing size and sophistication of computer systems, it is of the utmost importance that the equations that govern interconnection complexity are well defined and understood. This paper presents a new analysis of a hierarchical computer interconnection model that yields the analytical form of the interconnection distribution function. It is shown that this function is consistent with the previously derived equation for the average interconnection length and that the distribution function accurately describes the distribution of interconnections within previously constructed computer systems. The distribution function is then used to investigate the proposed relationship between the exponent of the Rent equation and the gradient of the length distribution function.