Vinay J. Ribeiro

A multifractal wavelet model with application to network traffic

We develop a new multiscale modeling framework for characterizing positive-valued data with long-range-dependent correlations (1/f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing N-point data sets. We study both the second-order and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variance-time plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.

Broadcast capacity in multihop wireless networks

In this paper we study the broadcast capacity of multihop wireless networks which we define as the maximum rate at which broadcast packets can be generated in the network such that all nodes receive the packets successfully in a limited time. We employ the Protocol Model for successful packet reception usually adopted in network capacity studies and provide novel upper and lower bounds for the broadcast capacity for arbitrary connected networks. In a homogeneous dense network these bounds simplify to Θ(W/max(1,Δd)) where W is the wireless channel capacity, Δ the interference parameter, and d the number of dimensions of space in which the network lies. Interestingly, we show that the broadcast capacity does not change by more than a constant factor when we vary the number of nodes, the radio range, the area of the network, and even the node mobility. To address the achievability of capacity, we demonstrate that any broadcast scheme based on a backbone of size proportional to the Minimum Connected Dominating Set guarantees a throughput within a constant factor of the broadcast capacity. Finally, we demonstrate that broadcast capacity, in stark contrast to unicast capacity, does not depend on the choice of source nodes or the dimension of the network.

Small-time scaling behaviors of Internet backbone traffic: an empirical study

The small-time (sub-seconds) scaling behaviors of Internet backbone traffic, based on traces collected from OC3/12/48 links in a tier-1 ISP is studied. We observe that for a majority of these traces, the (second-order) scaling exponents at small time scales (1 ms - 100 ms) are fairly close to 0.5, indicating that traffic fluctuations at these time scales are (nearly) uncorrelated. In addition, the traces manifest mostly monofractal behaviors at small time scales. The objective of the paper is to understand the potential causes or factors that influence the small-time scalings of Internet backbone traffic via empirical data analysis. We analyze the traffic composition of the traces along two dimensions - flow size and flow density. Our study uncovers dense flows (i.e., flows with bursts of densely clustered packets) as the correlation-causing factor in small time scales, and reveals that the traffic composition in terms of proportions of dense vs. sparse flows plays a major role in influencing the small-time scalings of aggregate traffic.

Strap-down Pedestrian Dead-Reckoning system

This paper presents a waist-worn Pedestrian Dead Reckoning (PDR) System that requires minimal end-user calibration. The PDR system is based on an Inertial Measurement Unit (IMU) comprising of a tri-axial accelerometer, a tri-axial magnetometer and a tri-axial gyroscope. We propose a novel heading estimation scheme using a quaternion-based extended Kalman filter (EKF) that estimates magnetic disturbances and corrects for them. Accelerometer measurements are used to detect step events and to estimate step lengths. Experimental results show that a relative distance error of about 3% to 8% can be obtained using our methods.

Locating available bandwidth bottlenecks

The spatio-temporal available bandwidth estimator (STAB), a new edge-based probing tool, locates thin links - those links with less available bandwidth than all the links preceding 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.

Simulation of nonGaussian long-range-dependent traffic using wavelets

In this paper, we develop a simple and powerful multiscale model for the synthesis of nonGaussian, long-range dependent (LRD) network traffic. Although wavelets effectively decorrelate LRD data, wavelet-based models have generally been restricted by a Gaussianity assumption that can be unrealistic for traffic. Using a multiplicative superstructure on top of the Haar wavelet transform, we exploit the decorrelating properties of wavelets while simultaneously capturing the positivity and “spikiness” of nonGaussian traffic. This leads to a swift O(N) algorithm for fitting and synthesizing N-point data sets. The resulting model belongs to the class of multifractal cascades, a set of processes with rich statistical properties. We elucidate our model’s ability to capture the covariance structure of real data and then fit it to real traffic traces. Queueing experiments demonstrate the accuracy of the model for matching real data. Our results indicate that the nonGaussian nature of traffic has a significant effect on queuing.

Color-Based Broadcasting for Ad Hoc Networks

This paper develops a novel color-based broadcast scheme for wireless ad hoc networks where each forwarding of the broadcast message is assigned a color from a given pool of colors. A node only forwards the message if it can assign it a color from the pool which it has not already overheard after a random time. In the closely related counter-based broadcast scheme a node simply counts the number of broadcasts not the colors overheard. The forwarding nodes form a so-called backbone, which is determined by the random timers and, thus, is random itself. Notably, any counter-generated backbone could result from pruning a color-generated backbone; the typical color-generated backbone, however, exhibits a connectivity graph richer than the counter-based ones. As a particular advantage, the colors reveal simple geometric properties of the backbones which we exploit to prove that the size of both, color- and counter-generated back-bones are within a small constant factor of the optimum. We also propose two techniques, boosting and edge-growing, that improve the performance of color- and counter-based broadcast in terms of reachability and number of rebroadcasts. Experiments reveal that the powerful boosting method is considerably more effective with the color-based schemes.

DRB and DCCB: Efficient and Robust Dynamic Broadcast for Ad Hoc and Sensor Networks

Deterministic, timer-based broadcast schemes not only guarantee full reachability over an idealistic lossless MAC layer, they also stand out for their robustness against node failure as well as more general changes in the network topology. This paper proposes the first broadcast schemes in this class which provably perform within a factor of the optimal efficiency (in terms of number of rebroadcasts). To the best of our knowledge no other deterministic timer-based scheme possesses this property. NS-2 simulations employing the 802.11b MAC protocol confirm our analysis. The factor can be estimated to be quite small. Novel to the proposed schemes is also their hybrid backbone consisting of a given, static dominating set (DS) and a dynamically computed set of connecting nodes. As an additional contribution, this paper studies the trade-off of timer settings (and thus latency) against the number of rebroadcasts, as well as the robustness of the proposed algorithms. To the best of our knowledge, no prior study of these issues in the context of broadcast exists.

Small-time scaling behavior of Internet backbone traffic

We perform an extensive wavelet analysis of Internet backbone traffic traces to observe and understand the causes of small-time scaling phenomena present in them. We observe that for a majority of the traces, the second-order scaling exponents at small time scales (1-100ms) are fairly close to 0.5, indicating that traffic fluctuations at these time scales are nearly uncorrelated. Some traces, however, do exhibit moderately large scaling exponents (~0.7) at small time scales. In addition, the traces manifest mostly monofractal behaviors at small time scales. To identify the network causes of the observed scaling behavior, we analyze the flow composition of the traffic along two dimensions-flow byte contribution and flow density. Our study points to the dense flows (i.e., flows with densely clustered packets) as the correlation-causing factor in small time scales, and reveals that the traffic composition in terms of proportions of dense vs. sparse flows plays a major role in influencing the small-time scalings of aggregate traffic. Since queuing inside routers is influenced by traffic fluctuations at small time-scales, our observations and results have important implications for networking modeling, service provisioning and traffic engineering.

Wavelets and multifractals for network traffic modeling and inference

This paper reviews the multifractal wavelet model (MWM) and its applications to network traffic modeling and inference. The discovery of the fractal nature of traffic has made new models and analysis tools for traffic essential, since classical Poisson and Markov models do not capture important fractal properties like multiscale variability and burstiness that deleteriously affect performance. Set in the framework of multiplicative cascades, the MWM provides a link to multifractal analysis, a natural tool to characterize burstiness. The simple structure of the MWM enables fast O(N) synthesis of traffic for simulations and a tractable queuing analysis, thus rendering it suitable for real networking applications including end-to-end path modeling.