The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena

The Internet is the most complex system ever created in human history. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for years. This paper is a review of the complex dynamics of Internet traffic. Departing from normal treatises, we will take a view from both the network engineering and physics perspectives showing the strengths and weaknesses as well as insights of both. In addition, many less covered phenomena such as traffic oscillations, large-scale effects of worm traffic, and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex System

Small and large scale behavior of moments of poisson cluster processes

Poisson cluster processes are special point processes that find use in modeling Internet traffic, neural spike trains, computer failure times and other real-life phenomena. The focus of this work is on the various moments and cumulants of Poisson cluster processes, and specifically on their behavior at small and large scales. Under suitable assumptions motivated by the multiscale behavior of Internet traffic, it is shown that all these various quantities satisfy scale free (scaling) relations at both small and large scales. Only some of these relations turn out to carry information about salient model parameters of interest, and consequently can be used in the inference of the scaling behavior of Poisson cluster processes. At large scales, the derived results complement those available in the literature on the distributional convergence of normalized Poisson cluster processes, and also bring forward a more practical interpretation of the so-called slow and fast growth regimes. Finally, the results are applied to a real data trace from Internet traffic.NSA grant [H98230-13-1-0220]info:eu-repo/semantics/publishedVersio

Strong approximations for time-varying infinite-server queues with non-renewal arrival and service processes

In real stochastic systems, the arrival and service processes may not be renewal processes. For example, in many telecommunication systems such as internet traffic where data traffic is bursty, the sequence of inter-arrival times and service times are often correlated and dependent. One way to model this non-renewal behavior is to use Markovian Arrival Processes (MAPs) and Markovian Service Processes (MSPs). MAPs and MSPs allow for inter-arrival and service times to be dependent, while providing the analytical tractability of simple Markov processes. To this end, we prove fluid and diffusion limits for MAP(t)/MSPt/ queues by constructing a new Poisson process representation for the queueing dynamics and leveraging strong approximations for Poisson processes. As a result, the fluid and diffusion limit theorems illuminate how the dependence structure of the arrival or service processes can affect the sample path behavior of the queueing process. Finally, our Poisson representation for MAPs and MSPs is useful for simulation purposes and may be of independent interest.111sciescopu

A comparison of Poisson and uniform sampling for active measurements

Copyright © 2006 IEEEActive probes of network performance represent samples of the underlying performance of a system. Some effort has gone into considering appropriate sampling patterns for such probes, i.e., there has been significant discussion of the importance of sampling using a Poisson process to avoid biases introduced by synchronization of system and measurements. However, there are unanswered questions about whether Poisson probing has costs in terms of sampling efficiency, and there is some misinformation about what types of inferences are possible with different probe patterns. This paper provides a quantitative comparison of two different sampling methods. This paper also shows that the irregularity in probing patterns is useful not just in avoiding synchronization, but also in determining frequency-domain properties of a system. This paper provides a firm basis for practitioners or researchers for making decisions about the type of sampling they should use in a particular applications, along with methods for the analysis of their outputs.Matthew Rougha