It is important to characterize the distributional property and the long-range dependency of traffic arrival processes in modeling Internet traffic. To address this problem, we propose a long-range dependent traffic model using the unbounded Johnson distribution. Using the proposed model, a sequence of traffic rates with the desired four quantiles and Hurst parameter can be generated. Numerical studies show how well the sequence of traffic rates generated by the proposed model mimics that of the real traffic rates using a publicly available Internet traffic trace.

Numerous studies have shown that scaling exponents of internet traffic change over time or scaling ranges. In order to analyze long-range dependent traffic with changing scaling exponents over time scales, we propose a multi-scale traffic model that incorporates the notion of a piecewise self-similar process, a process with spectral changes on its scaling behavior. We can obtain a performance curve smoothened over the range of queue length corresponding to time scales with different scaling exponents by adopting multiple self-similar processes piecewise into different spectra of time scale. The analytical method for the multiscale fractional Brownian motion is discussed as a model for this approach. A comparison of the analytical and simulation results, using traffic data obtained from backbone networks, shows that our model provides a good approximation for Gaussian traffic.

We study the statistical multiplexing performance of self-similar traffic. We consider that input streams have different QoS (Quality of Service) requirements such as loss and delay jitter. By applying the FBM (fractal Brownian motion) model, we present methods of estimating the effective bandwidth of aggregated traffic. We performed simulations to evaluate the QoS performances and the bandwidths required to satisfy them. The comparison between the estimation and the simulation confirms that the estimation could give rough data of the effective bandwidth. Finally, we analyze the bandwidth gain with priority multiplexing against non-prioritized multiplexing and suggest how to get better performance with the right configuration of QoS parameters.

This paper describes an analysis of IP-network traffic in terms of the time variation of self-similarity. To get a comprehensive view in analyzing the degree of long-range dependence (LRD) of IP-network traffic, this paper used a self-organizing map, which provides a way to map high-dimensional data onto a low-dimensional domain. Also, in the LRD-based analysis, this paper employed detrended fluctuation analysis (DFA), which is applicable to the analysis of long-range power-law correlations or LRD in non-stationary time-series signals. In applying this method to traffic analysis, this paper performed two kinds of traffic measurement: one based on IP-network traffic flowing into NTT Musashino R&D center (Tokyo, Japan) from the Internet and the other based on IP-network traffic flowing through at an interface point between an access provider (Tokyo, Japan) and the Internet. Based on sequential measurements of IP-network traffic, this paper derived corresponding values for the LRD-related parameter α of measured traffic. As a result, we found that the characteristic of self-similarity seen in the measured traffic fluctuated over time, with different time variation patterns for two measurement locations. In training the self-organizing map, this paper used three parameters: two α values for different plot ranges, and Shannon-based entropy, which reflects the degree of concentration of measured time-series data. We visually confirmed that the traffic data could be projected onto the map in accordance with the traffic properties, resulting in a combined depiction of the effects of the degree of LRD and network utilization rates. The proposed method can deal with multi-dimensional parameters, projecting its results onto a two-dimensional space in which the projected data positions give us an effective depiction of network conditions at different times.

As demonstrated by many studies, measured wide-area network traffic exhibits fractal properties, such as self-similarity, burstiness, and long-range dependence (LRD). In order to describe long-range dependent network traffic and to emphasize the performance aspects of descriptive traffic models with additive and multiplicative structures, the multifractal wavelet model (MWM), which is based on the binomial cascade, has been shown to match the behavior of network traffic over small and large time scales. In this paper, using appropriate mathematical and statistical analyses, we develop the MWM proposed in [14], which provides a complete description of long-range dependent network traffic. First, we present accurate parameters of the MWM over different time scales. Next, a marginal stable distribution of MWM network traffic data is analyzed. The accuracy of the proposed MWM compared to actual data measurements is confirmed by queuing behavior performance through computer simulations.

We examine the effectiveness of shaping and policing mechanisms in reducing the inherent variability of fractal traffic, with the objective of increasing network operating points. Whether a shaper simply spaces a flow or allows small bursts according to a leaky bucket, we show using analytical arguments that, i) the Hurst parameter, which describes the asymptotic variability of the traffic, is unaffected; and ii) while the traffic can be made smoother over time scales smaller than one corresponding to the shapers buffer size, fluctuations over longer time scales cannot be appreciably altered. We further show that if shaping is used to reduce buffer size requirements at a network bottleneck, any savings here are offset by the increased buffer requirements at the shapers. Perhaps the most significant deficiency of shaping identified here is that it is necessary to model individual streams to a level of accuracy that is not feasible in practice. In contrast, statistical multiplexing can achieve reasonable network efficiencies by only requiring characterizations of aggregate traffic.