Application of the many sources asymptotic in downscaling Internet-like Networks

In our earlier work by Fragkiskos Papadopoulos, et al. (2005), we have presented two methods to scale down the topology of the Internet, while preserving important performance metrics. We have shown that the methods can be used to greatly simplify and expedite performance prediction. The key insight that we have leveraged is that only the congested links along the path of each flow introduce sizable queueing delays and dependencies among flows. Based on this, we have shown that it is possible to infer the performance of the larger Internet by creating and observing a suitably scaled- down replica, consisting of the congested links only. However, two main assumptions of our approach were that uncongested links are known in advance, and that the queueing delays imposed by such links are negligible. In this paper we provide rules that can be used to identify uncongested links when these are not known, and we theoretically establish the conditions under which the negligible queueing delay assumption is valid. In particular, we first identify scenarios under which one can easily deduce whether a link imposes negligible queueing by inspecting the network topology. Then, we identify scenarios in which this is not possible and use known results based on the large deviations theory to approximate the queue length distribution. Finally, we use this approximation to decide which links are uncongested, and show that in the many- sources limit the queueing delays of uncongested links are indeed negligible. Our results are verified using simulations with TCP traffic.