Simplifying the synthesis of internet traffic matrices

A recent paper 8 presented methods for several steps along the road to synthesis of realistic traffic matrices. Such synthesis is needed because traffic matrices are a crucial input for testing many new networking algorithms, but traffic matrices themselves are generally kept secret by providers. Furthermore, even given traffic matrices from a real network, it is difficult to realistically adjust these to generate a range of scenarios (for instance for different network sizes). This note is concerned with the first step presented in 8: generation of a matrix with similar statistics to that of a real traffic matrix. The method applied in 8 is based on fitting a large number of distributions, and finding that the log-normal distribution appears to fit most consistently. Best fits (without some intuitive explanation for the fit) are fraught with problems. How general are the results? How do the distribution parameters relate? This note presents a simpler approach based on a gravity model. Its simplicity provides us with a better understanding of the origins of the results of 8, and this insight is useful, particularly because it allows one to adapt the synthesis process to different scenarios in a more intuitive manner. Additionally, 8 measures the quality of its fit to the distribution's body. This note shows that the tails of the distributions are less heavy than the log-normal distribution (a counterintuitive result for Internet traffic), and that the gravity model replicates these tails more accurately.