Evolution of the internet map and load distribution

Abstract

We track the evolutionary history of the Internet at the autonomous systems (ASes) level and provide the evidence that it can be described in the framework of the multiplicative stochastic process. It is found that the fluctuations arising in the process of diversifying connections of each node play an essential role in forming the status quo of the Internet. Extracting relevant parameters for the growth dynamics of the Internet topology, we are able to predict the connectivity (degree) exponent 7 of the Internet AS map successfully. We also introduce a quantity called the load as the capacity of node needed for handling the communication traffic and study its distribution over the Internet across years. The load distribution follows a power law with the exponent δ ≈ 2.0 and the load at the hub scales with the network size as ℓh ∼ N1.8. © Springer-Verlag 2004.