Rudolf H. Riedi

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.

Multiscale nature of network traffic

The complexity and richness of telecommunications traffic is such that one may despair to find any regularity or explanatory principles. Nonetheless, the discovery of scaling behavior in teletraffic has provided hope that parsimonious models can be found. The statistics of scaling behavior present many challenges, especially in nonstationary environments. In this article, we overview the state of the art in this area, focusing on the capabilities of the wavelet transform as a key tool for unraveling the mysteries of traffic statistics and dynamics.

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.

Connection-level analysis and modeling of network traffic

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 traffic. 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 traffic 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.

In search of invariants for e-business workloads

ABSTRACT Understanding the nature and hara teristi s of e-business workloads is a ru ial step to improve the quality of servi e o ered to ustomers in ele troni business environments. However, the variety and omplexity of the intera tions between ustomers and sites make the hara terization of ebusiness workloads a hallenging problem. Using a multilayer hierar hi al model, this paper presents a detailed hara terization of the workload of two a tual e-business sites: an online bookstore and an ele troni au tion site. Through the hara terization pro ess, we found the presen e of autonomous agents, or robots, in the workload and used the hierar hi al stru ture to determine their hara teristi s. We also found that sear h terms follow a Zipf distribution.

Measurement based analysis, modeling, and synthesis of the internet delay space

Understanding the characteristics of the Internet delay space (i.e., the all-pairs set of static round-trip propagation delays among edge networks in the Internet) is important for the design of global-scale distributed systems. For instance, algorithms used in overlay networks are often sensitive to violations of the triangle inequality and to the growth properties within the Internet delay space. Since designers of distributed systems often rely on simulation and emulation to study design alternatives, they need a realistic model of the Internet delay space. In this paper, we analyze measured delay spaces among thousands of Internet edge networks and quantify key properties that are important for distributed system design. Our analysis shows that existing delay space models do not adequately capture these important properties of the Internet delay space. Furthermore, we derive a simple model of the Internet delay space based on our analytical findings. This model preserves the relevant metrics far better than existing models, allows for a compact representation, and can be used to synthesize delay data for simulations and emulations at a scale where direct measurement and storage are impractical. We present the design of a publicly available delay space synthesizer tool called DS 2 and demonstrate its effectiveness.

TCP-Africa: an adaptive and fair rapid increase rule for scalable TCP

High capacity data transfers over the Internet routinely fail to meet end-to-end performance expectations. The default transport control protocol for best effort data traffic is currently TCP, which does not scale well to 100 Mbps and higher networks over long distances. In congestion avoidance, TCP is not swift enough to fully utilize resources over paths with a high delay bandwidth product. First attempts to alleviate this problem by equipping TCP with increased aggressiveness have shown the disadvantage of poor fairness with the ubiquitous standard TCP-Reno, or in some cases, even among two connections running over the same path. We propose a new delay sensitive-congestion avoidance mode (TCP-Africa) that allows for scalable, aggressive behavior in large underutilized links, yet falls back to the more conservative TCP-Reno algorithm once links become well utilized and congestion is imminent. Through ns2 simulations we argue for the safety, efficiency, and fairness of TCP-Africa.

On non-scale-invariant infinitely divisible cascades

Multiplicative processes, multifractals, and more recently also infinitely divisible cascades have seen increased popularity in a host of applications requiring versatile multiscale models, ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. The methodologies prevalent as of today rely to a large extent on iterative schemes used to produce infinite detail and repetitive structure across scales. While appealing, due to their simplicity, these constructions have limited applicability as they lead by default to power-law progression of moments through scales, to nonstationary increments and often to inherent log-periodic scaling which favors an exponential set of scales. This paper studies and develops a wide class of infinitely divisible cascades (IDC), thereby establishing the first reported cases of controllable scaling of moments in non-power-law form. Embedded in the framework of IDC, these processes exhibit stationary increments and scaling over a continuous range of scales. Criteria for convergence, further statistical properties, as well as MATLAB routines are provided.

Fractional Brownian motion and data traffic modeling: The other end of the spectrum

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.

Bounds for the capacity of wireless multihop networks imposed by topology and demand

Existing work on the capacity of wireless networks predominantly considers homogeneous random networks with random work load. The most relevant bounds on the network capacity, e.g., take into account only the number of nodes and the area of the network. However, these bounds can significantly overestimate the achievable capacity in real world situations where network topology or traffic patterns often deviate from these simplistic assumptions. To provide analytically tractable yet asymptotically tight approximations of network capacity we propose a novel space-based approach. At the heart of our methodology lie simple functions which indicate the presence of active transmissions near any given location in the network and which constitute a tool well suited to untangle the interactions of simultaneous transmissions. We are able to provide capacity bounds which are tighter than the traditional ones and which involve topology and traffic patterns explicitly, e.g., through the length of Euclidean Minimum Spanning Tree, or through traffic demands between clusters of nodes. As an additional novelty our results cover unicast, multicast and broadcast and are asymptotically tight. Notably, our capacity bounds are simple enough to require only knowledge of node location, and there is no need for solving or optimizing multi-variable equations in our approach.