Investigating self-similarity and heavy tailed distributions on a large scale experimental facility

After seminal work by Taqqu et al. relating self-similarity to heavy tail distributions, a number of research articles verified that aggregated Internet traffic time series show self-similarity and that Internet attributes, like WEB file sizes and flow lengths, were heavy tailed. However, the validation of the theoretical prediction relating self-similarity and heavy tails remains unsatisfactorily addressed, being investigated either using numerical or network simulations, or from uncontrolled web traffic data. Notably, this prediction has never been conclusively verified on real networks using controlled and stationary scenarii, prescribing specific heavy-tail distributions, and estimating confidence intervals. In the present work, we use the potential and facilities offered by the large-scale, deeply reconfigurable and fully controllable experimental Grid5000 instrument, to investigate the prediction observability on real networks. To this end we organize a large number of controlled traffic circulation sessions on a nation-wide real network involving two hundred independent hosts. We use a FPGA-based measurement system, to collect the corresponding traffic at packet level. We then estimate both the self-similarity exponent of the aggregated time series and the heavy-tail index of flow size distributions, independently. Comparison of these two estimated parameters, enables us to discuss the practical applicability conditions of the theoretical prediction

Investigating self-similarity and heavy-tailed distributions on a large scale experimental facility

International audienceAfter the seminal work by Taqqu et al. relating selfsimilarity to heavy-tailed distributions, a number of research articles verified that aggregated Internet traffic time series show self-similarity and that Internet attributes, like Web file sizes and flow lengths, were heavy-tailed. However, the validation of the theoretical prediction relating self-similarity and heavy tails remains unsatisfactorily addressed, being investigated either using numerical or network simulations, or from uncontrolled Web traffic data. Notably, this prediction has never been conclusively verified on real networks using controlled and stationary scenarii, prescribing specific heavy-tailed distributions, and estimating confidence intervals. With this goal in mind, we use the potential and facilities offered by the large-scale, deeply reconfigurable and fully controllable experimental Grid5000 instrument, to investigate the prediction observability on real networks. To this end we organize a large number of controlled traffic circulation sessions on a nation-wide real network involving two hundred independent hosts. We use a FPGA-based measurement system, to collect the corresponding traffic at packet level. We then estimate both the self-similarity exponent of the aggregated time series and the heavy-tail index of flow size distributions, independently. On the one hand, our results complement and validate with a striking accuracy some conclusions drawn from a series of pioneer studies. On the other hand, they bring in new insights on the controversial role of certain components of real networks

Tail Dependence for Regularly Varying Time Series

We use tail dependence functions to study tail dependence for regularly varying RV time series. First, tail dependence functions about RV time series are deduced through the intensity measure. Then, the relation between the tail dependence function and the intensity measure is established: they are biuniquely determined. Finally, we obtain the expressions of the tail dependence parameters based on the expectation of the RV components of the time series. These expressions are coincided with those obtained by the conditional probability. Some simulation examples are demonstrated to verify the results we established in this paper

Revisiting an old friend: On the observability of the relation between Long Range Dependence and Heavy Tail

International audienceTaqqu's Theorem plays a fundamental role in Internet traffic modeling, for two reasons: First, its theoretical formulation matches closely and in a meaningful manner some of the key network mechanisms controlling traffic characteristics; Second, it offers a plau- sible explanation for the origin of the long range dependence property in relation with the heavy tail nature of the traffic components. Numerous attempts have since been made to observe its predictions empirically, either from real Internet traffic data or from numerical simulations based on popular traffic models, yet rarely has this resulted in a satisfactory quantitative agreement. This raised in the literature a number of comments and questions, ranging from the adequacy of the theorem to real world data to the relevance of the statistical tools involved in practical analyses. The present contribution aims at studying under which conditions this fundamental theorem can be actually seen at work on real or simulated data. To do so, numerical simulations based on standard traffic models are analyzed in a wavelet framework. The key time scales involved are derived, enabling a discussion of the origin and nature of the difficulties encountered in attempts to empirically observe Taqqu's Theorem

Wavelet Spectrum for Investigating Statistical Characteristics of UDP-Based Internet Traffic

In this paper, we consider statistical characteristics of real User Datagram Protocol (UDP) traffic. Four main issues in the study include(i) the presence of long rangedependence (LRD) in the UDP traffic,(ii) the marginal distribution of the UDP traces,(iii) dependence structure of wavelet coefficients,(iv) and performance evaluation of the Hurst parameter estimation based on different numbers of vanishing moments of the mother wavelet. By analyzing a large set of real traffic data, it is evident that the UDP Internet traffic reveals the LRD properties with considerably high non-stationary processes.Furthermore, it exhibits non-Gaussian marginal distributions. However, by increasing the number of vanishing moments,it is impossible to achieve reduction fromLRD to become a short range dependence. Thus, it can be shown that there is no significant difference in performance estimation of the Hurst parameter for different numbers of vanishing moments of the mother wavelet

On the Distribution of Traffic Volumes in the Internet and its Implications

In this edition of the Voice, the College’s Career Planning Placement Service offers a variety or workshops include one on life planning. Wooster Chief of Security and Dr. Startzman of the campus wellness center, speak to students on the topic of rape and safety at the College. The Wooster Board of Trustees begins the process to select a new president of the College of Wooster. The Art Center offers classes on quilting, plants, printmaking, drawing, and other artistic mediums, to students for eight weeks. Additionally, an article discusses the, then up and coming, Bicentennial of the United States.https://openworks.wooster.edu/voice1971-1980/1131/thumbnail.jp

Abstract Description of Internet Traffic of Generalized Cauchy Type

Self-similar process with long-range dependence (LRD), that is, fractional Gaussian noise (fGn) with LRD is a widely used model of Internet traffic. It is indexed by its Hurst parameter HfGn that linearly relates to its fractal dimension DfGn. Note that, on the one hand, the fractal dimension D of traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is characterized by its Hurst parameter H. However, by using fGn, both the self-similarity and the LRD of traffic are measured by HfGn . Therefore, there is a limitation for fGn to accurately model traffic. Recently, the generalized Cauchy (GC) process was introduced to model traffic with the flexibility to separately measure the fractal dimension DGC and the Hurst parameter HGC of traffic. However, there is a fundamental problem whether or not there exists the generality that the GC model is more conformable with real traffic than single parameter models, such as fGn, irrelevant of traffic traces used in experimental verification. The solution to that problem remains unknown but is desired for model evaluation in traffic theory or for model selection against specific issues, such as queuing analysis relating to the autocorrelation function (ACF) of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 3.17) with the following features in analysis. (i) Set-valued analysis of the traffic of the fGn type. (ii) Set-valued analysis of the traffic of the GC type. (iii) Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type