The problem of synthetically generating IP traffic matrices: Initial recommendations

There exist a wide variety of network design problems that require a traffic matrix as input in order to carry out performance evaluation. The research community has not had at its disposal any information about how to construct realistic traffic matrices. We introduce here the two basic problems that need to be addressed to construct such matrices. The first is that of synthetically generating traffic volume levels that obey spatial and temporal patterns as observed in realistic traffic matrices. The second is that of assigning a set of numbers (representing traffic levels) to particular node pairs in a given topology. This paper provides an in-depth discussion of the many issues that arise when addressing these problems. Our approach to the first problem is to extract statistical characteristics for such traffic from real data collected inside two large IP backbones. We dispel the myth that uniform distributions can be used to randomly generate numbers for populating a traffic matrix. Instead, we show that the lognormal distribution is better for this purpose as it describes well the mean rates of origin-destination flows. We provide estimates for the mean and variance properties of the traffic matrix flows from our datasets. We explain the second problem and discuss the notion of a traffic matrix being well-matched to a topology. We provide two initial solutions to this problem, one using an ILP formulation that incorporates simple and well formed constraints. Our second solution is a heuristic one that incorporates more challenging constraints coming from carrier practices used to design and evolve topologies.