The analytical form of the length distribution function for computer interconnection

An analysis of a hierarchical computer interconnection model that yields the analytical form of the interconnection distribution function is presented. 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. It is confirmed that the pin-limited partitioning of computer systems results in an approximate power-law length distribution function, and for large numbers of gates the characteristic exponent of the length distribution function γ is related to the Rent exponent by γ≈3-2 p. In addition, it is shown that the theoretical equations are a good approximation to experimentally observed interconnection distributions