In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with longrange-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 Npoint 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.

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, ∆ d )) where W is the wireless channel capacity, ∆ 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.

Abstract-Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of long-range dependence (LRD) and marginal statistics still remains on unsure footing. In this paper, we study these two issues by introducing a multiscale traffic model and a novel multiscale approach to queuing analysis. The multifractal wavelet model (MWM) is a multiplicative, wavelet-based model that captures the positivity, LRD, and "spikiness" of non-Gaussian traffic. Using a binary tree, the model synthesizes an N-point data set with only 0 (N) computations.Leveraging the tree structure of the model, we derive a multiscale queuing analysis that provides a simple closed form approximation to the tail queue probability, valid for any given buffer size. The analysis is applicable. not only to the MWM but to tree-based models in general, including fractional Gaussian noise. Simulated queuing experiments demonstrate the accuracy of the MWM for matching real data traces and the precision of our theoretical queuing formula. Thus, the MWM is useful not only for fast synthesis of data for simulation purposes but also for applications requiring accurate queuing formulas such as call admission control. Our results clearly indicate that the marginal distribution of traffic at different time-resolutions affects queuing and that a Gaussian assumption can lead to over-optimistic predictions of tail queue probability even when taking LRD into account.

Abstract-We 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. We observe that for a majority of these traces, the (second-order) scaling exponents at small time scales (1ms -100ms) 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 smalltime 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.

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