R-3 Repository :: Browsing by Author "Riedi, Rudolf H."

Browsing by Author "Riedi, Rudolf H."

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Additive and Multiplicative Mixture Trees for Network Traffic Modeling
(2002-05-01) Sarvotham, Shriram; Wang, Xuguang; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and long range dependence at very large time scales to highly non-Gaussian marginals and multifractal scaling on small scales. This behavior can be explained by forming two components of the traffic according to the speed of connections, one component absorbing most traffic and being mostly Gaussian, the other constituting virtually all the small scale bursts. Towards a better understanding of this phenomenon, we propose a novel tree-based model which is flexible enough to accommodate Gaussian as well as bursty behavior on different scales in a parsimonious way.
Analysis of Safari: An architecture for scalable ad hoc networking and services
(2004) Mohammed, Ahamed Khan; Riedi, Rudolf H.
The convenience, utility value, and ease of deployment has led to an ubiquitous integration of mobile computing devices which will, in future, form mobile ad hoc networks (MANETs), several orders of magnitude larger than what current protocols can handle. Safari, a scalable ad hoc networking architecture, promises to provide scalable routing and conventional internet services like SMTP and DNS in ad hoc networks of the size of 10's of thousands of nodes. Firstly, this thesis analyzes the buoy protocol which assigns spatially meaningful hierarchical addresses to nodes in Safari, specifically its stability and convergence properties. Secondly, it characterizes some of the control overhead in Safari by leveraging physical models whose applicability is demonstrated through simulations. This leads to insights on parameter settings and design choices in the Safari architecture to reduce overhead, a necessary feature in the bandwidth and energy limited ad hoc network environment.
Compound Poisson Cascades
(2002-05-01) Chainais , Pierre; Riedi, Rudolf H.; Abry, Patrice; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic, to name but two. Placing multifractal analysis in the more general framework of infinitely divisible laws, we design processes which possess at the same time stationary increments as well as multifractal and more general infinitely divisible scaling over a continuous range of scales. The construction is based on a Poissonian geometry to allow for continuous multiplication. As they possess compound Poissonian statistics we term the resulting processes compound Poisson cascades. We explain how to tune their correlation structure, as well as their scaling properties, and hint at how to go beyond scaling in form of pure power laws towards more general infinitely divisible scaling. Further, we point out that these cascades represent but the most simple and most intuitive case out of an entire array of infinitely divisible cascades allowing to construct general infinitely divisible processes with interesting scaling properties.
Conditional and Relative Multifractal Spectra
(1997-03-01) Riedi, Rudolf H.; Scheuring, Istvan; Digital Signal Processing (http://dsp.rice.edu/)
In the study of the involved geometry of singular distributions the use of fractal and multifractal analysis has shown results of outstanding significance. So far, the investigation has focused on structures produced by one single mechanism which were analyzed with respect to the ordinary metric or volume. Most prominent examples include self-similar measures and attractors of dynamical systems. In certain cases, the multifractal spectrum is known explicitly, providing a characterization in terms of the geometrical properties of the singularities of a distribution. Unfortunately, strikingly different measures may possess identical spectra. To overcome this drawback we propose two novel methods, the conditional and the relative multifractal spectrum, which allow for a direct comparison of two distributions. These notions measure the extent to which the singularities of two distributions 'correlate'. Being based on multifractal concepts, however, they go beyond calculating correlations. As a particularly useful tool we develop the multifractal formalism and establish some basic properties of the new notions. With the simple example of Binomial multifractals we demonstrate how in the novel approach a distribution mimics a metric different from the usual one. Finally, the provided applications to real data show how to interpret the spectra in terms of mutual influence of dense and sparse parts of the distributions.
Connection-level Analysis and Modeling of Network Traffic
(2001-11-01) Sarvotham, Shriram; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
Most network traffic analysis and modeling studies lump all connections together into a single flow. Such aggregate traffic typically exhibits long-range-dependent (LRD) correlations and non-Gaussian marginal distributions. Importantly, in a typical aggregate traffic model, traffic bursts arise from many connections being active simultaneously. In this paper, we develop a new framework for analyzing and modeling network traffic that moves beyond aggregation by incorporating connection-level information. A careful study of many traffic traces acquired in different networking situations reveals (in opposition to the aggregate modeling ideal) that traffic bursts typically arise from just a few high-volume connections that dominate all others. We term such dominating connections alpha traflc. Alpha traffic is caused by large file transmissions over high bandwidth links and is extremely bursty (non-Gaussian). Stripping the alpha traffic from an aggregate trace leaves a beta traf/ic residual that is Gaussian, LRD, and shares the same fractal scaling exponent as the aggregate traffic. Beta traffic is caused by both small and large file transmissions over low bandwidth links. In our alpha/beta traffic model, the heterogeneity of the network resources give rise to burstiness and heavy-tailed connection durations give rise to LRD. Queuing experiments suggest that the alpha component dictates the tail queue behavior for large queue sizes, whereas the beta component controls the tail queue behavior for small queue sizes.
Diverging moments and parameter estimation
(2004-01-15) Goncalves, Paulo; Riedi, Rudolf H.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Heavy tailed distributions enjoy increased popularity and become more readily applicable as the arsenal of analytical and numerical tools grows. They play key roles in modeling approaches in networking, finance, hydrology to name but a few. The tail parameter is of central importance as it governs both the existence of moments of positive order and the thickness of the tails of the distribution. Some of the best known tail estimators such as Koutrouvelis and Hill are either parametric or show lack in robustness or accuracy. This paper develops a shift and scale invariant, non-parametric estimator for both, upper and lower bounds for orders with finite moments. The estimator builds on the equivalence between tail behavior and the regularity of the characteristic function at the origin and achieves its goal by deriving a simplified wavelet analysis which is particularly suited to characteristic functions.
Effect of the traffic bursts in the network queue
(2004) KeshavarzHaddad, Alireza; Riedi, Rudolf H.
This thesis studies the effect of the traffic bursts in the queue. Knowledge of the queueing behavior provides opportunity for additional control and improved performance. Most existing work on queueing today is based on Long-Range-Dependence (LRD) and Self-similarity, two well-known properties of network traffic at large scales. However, network traffic shows bursty behavior on small scales which are not captured by traditional self-similar models. We leverage a decomposition of traffic into two components. The alpha component is the bursty part of the traffic consisting of only few high bandwidth connections. The beta component collects the residual traffic and is a Gaussian LRD process. The alpha component is highly non-Gaussian and bursty. We propose two models for the alpha component, a heavy-tailed self-similar process and a high rate ON/OFF source. Our results explain how size and type of bursts affect the queueing behavior.
Exceptions to the Multifractal Formalism for Discontinuous Measures
(1998-01-15) Riedi, Rudolf H.; Mandelbrot, Benoit; Digital Signal Processing (http://dsp.rice.edu/)
In an earlier paper the authors introduced the inverse measure Âµ^â(dt) of a given measure Âµ(dt) on [0,1] and presented the 'inversion formula' f^â(a) = af(1/a) which was argued to link the respective multifractal spectra of Âµ and Âµ^â. A second paper established the formula under the assumption that Âµ and Âµ^â are continuous measures. Here, we investigate the general case which reveals telling details of interest to the full understanding of multifractals. Subjecting self-similar measures to the operation Âµ->Âµ^â creates a new class of discontinuous multifractals. Calculating explicitly we find that the inversion formula holds only for the 'fine multifractal spectra' and not for the 'coarse' ones. As a consequence, the multifractal formalism fails for this class of measures. A natural explanation is found when drawing parallels to equilibrium measures of dynamical systems. In the context of our work it becomes natural to consider the degenerate HÃ¶lder exponents 0 and infinity.
Explicit Lower Bounds of the Hausdorff Dimension of Certain Self Affine Sets
(1995-01-20) Riedi, Rudolf H.; Digital Signal Processing (http://dsp.rice.edu/)
A lower bound of the Hausdorff dimension of certain self-affine sets is given. Moreover, this and other known bounds such as the box dimension are expressed in terms of solutions of simple equations involving the singular values of the affinities.
Fractional Brownian motion and data traffic modeling: The other end of the spectrum
(1997-01-20) Vehel, Jacques; Riedi, Rudolf H.; Digital Signal Processing (http://dsp.rice.edu/)
We analyze the fractal behavior of the high frequency part of the Fourier spectrum of fBm using multifractal analysis and show that it is not consistent with what is measured on real traffic traces. We propose two extensions of fBm which come closer to actual traffic traces multifractal properties.
A Hierarchical and Multiscale Analysis of E-Business Workloads
(2002-01-15) Menascé, Daniel; Almeida, Virgilio; Riedi, Rudolf H.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Understanding the nature and characteristics of E-business workloads is a crucial step to improve the quality of service offered to customers in electronic business environments. Using a multi-layer hierarchical model, this paper presents a detailed multiscale characterization of the workload of two actual E-business sites: an online bookstore and an electronic auction site. Our analysis of the workloads showed that the session length, measured in number of requests to execute E-business functions, is heavy-tailed, especially for sites subject to requests generated by robots. An overwhelming majority of the sessions consists of only a handful requests. This seems to suggest that most customers are human (as opposed to robots). A significant fraction of the functions requested by customers were found to be product selection functions as opposed to product ordering. An analysis of the popularity of search terms revealed that it follows a Zipf distribution. However, Zipf's law as applied to E-business is time scale dependent due to the shift in popularity of search terms. We also found that requests to execute frequent E-business functions exhibit a similar pattern of behavior as observed for the total number of HTTP requests. Finally, our analysis demonstrated that there is a strong correlation in the arrival process at the HTTP request level. These correlations are particularly stronger at intermediate time scales of a few minutes.
An Improved Multifractal Formalism and Self Affine Measures
(1993-01-20) Riedi, Rudolf H.; Digital Signal Processing (http://dsp.rice.edu/)
This document is a six page summary of my Ph.D. thesis in which multifractal formalism based on counting on coarse levels (as opposed to a dimensional approach) is developed. This formalism is then applied to self-affine measures discovering phase transitions which are not present with self-similar measures.
An Improved Multifractal Formalism and Self Similar Measures
(1995-01-01) Riedi, Rudolf H.; Digital Signal Processing (http://dsp.rice.edu/)
To characterize the geometry of a measure, its so-called generalized dimensions D(q) have been introduced recently. The mathematically precise definition given by Falconer turns out to be unsatisfactory for reasons of convergence as well as of undesired sensitivity to the particular choice of coordinates in the negative q range. A new definition is introduced, which is based on box-counting too, but which carries relevant information also for negative q. In particular, rigorous proofs are provided for the Legendre connection between generalized dimensions and the so-called multifractal spectrum and for the implicit formula giving the generalized dimensions of self-similar measures, which was until now known only for positive q.
An introduction to multifractals
(1997-01-15) Riedi, Rudolf H.; Digital Signal Processing (http://dsp.rice.edu/)
This is an easy read introduction to multifractals. We start with a thorough study of the Binomial measure from a multifractal point of view, introducing the main multifractal tools. We then continue by showing how to generate more general multiplicative measures and close by presenting an extensive set of examples on which we elaborate how to 'read' a multifractal spectrum.
Inverse Measures, the Inversion formula, and Discontinuous Multifractals
(1997-01-20) Mandelbrot, Benoit; Riedi, Rudolf H.; Digital Signal Processing (http://dsp.rice.edu/)
The present paper is part I of a series of three closely related papers in which the inverse measure m' of a given measure m on [0,1] is introduced. In the first case discussed in detail, both these measures are multifractal in the usual sense, that is, both are linearly self-similar and continuous but not differentiable and both are non-zero for every interval of [0,1]. Under these assumptions the HÃ¶lder multifractal spectra of the two measures are shown to be linked by the inversion formula f'(a) = a f(1/a) . The inversion formula is then subjected to several diverse variations, which reveal telling details of interest to the full understanding of multifractals. The inverse of the uniform measure on a Cantor dust leads us to argue that this inversion formula applies to the Hausdorff spectrum even if the measures m and m' are not continuous while it may fail for the spectrum obtained by the Legendre path. This phenomenon goes along with a loss of concavity in the spectrum. Moreover, with the examples discussed it becomes natural to include the degenerate HÃ¶lder exponents 0 and infinity in the HÃ¶lder spectra. This present paper is the first of three closely related papers on inverse measures, introducing the new notion in a language adopted for the physicist. Parts II and III make rigorous what is argued with intuitive arguments here. Part II extends the common scope of the notion of self-similar measures. With this broader class of invariant measures part III shows that the multifractal formalism may fail.
Inversion Formula for Continuous Multifractals
(1997-01-20) Riedi, Rudolf H.; Mandelbrot, Benoit; Digital Signal Processing (http://dsp.rice.edu/)
In a previous paper the authors introduced the inverse measure Âµ^â of a probability measure Âµ on [0,1]. It was argued that the respective multifractal spectra are linked by the 'inversion formula' f^â(a) = af(1/a). Here, the statements of Part I are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures. Thereby, f may stand for the Hausdorff spectrum, the pacing spectrum, or the coarse grained spectrum. With a closer look at the special case of self-similar measures we offer a motivation of the inversion formula as well as a discussion of possible generalizations. Doing so we find a natural extension of the scope of the notion 'self-similar' and a failure of the usual multifractal formalism.
Locating Available Bandwidth Bottlenecks
(2004-09-01) Ribeiro, Vinay Joseph; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
The Spatio-temporal Available Bandwidth estimator (STAB), a new edge-based probing tool, locates thin links --- those links with less available bandwidth than all links preceeding them --- on end-to-end network paths. By localizing thin links, STAB facilitates network operations and troubleshooting, provides insight into what causes network congestion, and aids network-aware applications. The tool uses special chirp probing trains, featuring an exponential flight pattern of packets, which have the advantage of employing few packets while giving an accurate estimate of available bandwidth.
Long-Range Dependence: Now you see it now you don't!
(2002-11-20) Karagiannis , Thomas; Faloutsos , Michalis; Riedi, Rudolf H.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
Over the last few years, the network community has started to rely heavily on the use of novel concepts such as self-similarity and Long-Range Dependence (LRD). Despite their wide use, there is still much confusion regarding the identification of such phenomena in real network traffic data. In this paper, we show that estimating Long Range Dependence is not straightforward: there is no systematic or definitive methodology. There exist several estimating methodologies, but they can give misleading and conflicting estimates. More specifically, we arrive at several conclusions that could provide guidelines for a systematic approach to LRD. First, long-range dependence may exist even, if the estimators have different estimates in value. Second, long-range dependence is unlikely to exist, if there are several estimators that do not ``converge'' statistically to a value. Third, we show that periodicity can obscure the analysis of a signal giving partial evidence of long range dependence. Fourth, the Whittle estimator is the most accurate in finding the exact value when LRD exists, but it can be fooled easily by periodicity. As a case-study, we analyze real round-trip time data. We find and remove a periodic component from the signal, before we can identify long-range dependence in the remaining signal.
Measurement-Based Analysis, Modeling, and Synthesis of the Internet Delay Space for Large Scale Simulation
(2006-10-04) Zhang, Bo; Ng, T. S. Eugene; Nandi, Animesh; Riedi, Rudolf H.; Druschel, Peter; Wang, Guohui
The characteristics of packet delays among edge networks in the Internet can have a significant impact on the performance and scalability of global-scale distributed systems. Designers rely on simulation to study design alternatives for such systems at scale, which requires an appropriate model of the Internet delay space. The model must preserve the geometry and density distribution of the delay space, which are known, for instance, to influence the effectiveness of selforganization algorithms used in overlay networks. In this paper, we characterize measured delays between Internet edge networks with respect to a set of relevant metrics. We show that existing Internet models differ dramatically from measured delays relative to these metrics. Then, based on measured data, we derive a model of the Internet delay space. The model preserves the relevant metrics, allows for a compact representation, and can be used to synthesize delay data for large-scale simulations. Moreover, specific metrics of the delay space can be adjusted in a principled manner, thus allowing systems designers to study the robustness of their designs to such variations.
Modeling price dynamics on electronic stock exchanges with applications in developing automated trading strategies
(2009) Gershman, Darrin Matthew; Riedi, Rudolf H.
This thesis develops models for accurate prediction of price changes on electronic stock exchanges by utilizing autoregressive and logistic methods. Prices on these electronic stock exchanges, also called ECNs, are solely determined by where orders have been placed into the order book, unlike traditional stock exchanges where prices are determined by an expert market maker. Identifying the significant variables and formulating the models will provide critical insight into the dynamics of prices on ECNs. Whereas previous research has relied on simulated data to test market strategies, this analysis will utilize actual ECN data. The models recognize patterns of asymmetry and movement of the shares in the order book to formulate accurate probabilities for possible future price changes. On traditional stock exchanges, price changes could only occur as quickly as human beings could enact them. On ECNs, computerized systems place orders on behalf of traders based on their preferences, resulting in price changes that reflect trader activity almost instantaneously. The quickness of this automation on ECNs forces the re-evaluation of commonly held beliefs about stock price dynamics. Previous strategies developed for trading on ECNs have relied mainly on price fluctuations to gain profits. This thesis uses the formulated models to design profitable strategies that use accurate prediction rather than price variability.

Browsing by Author "Riedi, Rudolf H."

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