Feedback-induced Packet Delay Dynamics in Power-law Networks

As the Internet becomes a social infrastructure of information exchange and global communication, many network devices are connected to the Internet and many users communicate via the Internet. Although, OSI’s functional partition for network-related protocols makes various Internet to be distributed, large-scaled communication systems, dynamic interactions of the networkrelated protocols, induced by the functional partition also make the Internet to be an complicated systems. One of complex behaviors of the Internet is traffic dynamics. For example, flow control and congestion control performed by end host can show short-range and long-range dependence of traffic. The Internet is facing with ever-changing networking technologies and applications, so understanding and controlling the complex behaviors of the Internet are important in designing the network. Although the statistical property of network traffic is hard to capture, measurement studies of the Internet topology revealed that the degree distributions of the Internet topologies follow a power law. That is, existing probability of nodes having k links is proportional to k−γ . A powerlaw relation often appears in many complex systems, e.g., biological systems, brain systems, and some engineering systems. Thus, complex networks where their topology is formed based on the interaction between individuals of the network have been interested in recent years. The BA model and its variants are widely used in many studies concerned about power-law networks. However, only the power-law degree distribution does not determine network-level performance of networking methods. That is, the structural characteristics of topologies other than the degree distribution are essential to discuss the behavior of networking methods. In this thesis, we investigate traffic dynamics on ISP’s router-level topology where the degree distribution exhibits power-law attribute and each of the nodes interacts via end-to-end flow control functionality. In previous studies, the relationship between statistical properties of the Internet 1 traffic and end-to-end flow control has been discussed. However, these researches deal with simple small topologies. We therefore investigate how structure of topologies impacts on traffic dynamics. We first show packet delay dynamics on the BA topology generated by the BA model and the ISP’s router-level topology. We then discuss how structure of topologies and flow controls affect the endto-end packet delay distribution and the queue length fluctuation of links. Extensive simulation results show that the end-to-end packet delay distributions exhibit a heavy tail by the TCP model. Moreover, the number of links that are highly fluctuated is more than twice comparing to the results of the stop-and-wait model. In the TCP model, 10% of total links are highly fluctuated when the number of session is large. When the number of session is small, 0.8% of total links are highly fluctuated. The results also indicate the queue length fluctuation disappears at bottleneck links and appears their tributary links due to the modularity structure of ISP’s router-level topology. Even in this case, the modularity structure of the AT&T topology reduces the number of highly fluctuated link up to 40% comparing to the results of the BA topology.