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.

In this letter, we propose a video traffic model based on a class of stochastic processes, which we call truncated GeoY/G/∞ input processes. Group of picture (GOP) size traces are modeled by truncated GeoY/G/∞ input process with gamma-distributed batch sizes Y and Weibull-like autocorrelation function. With full-length MPEG-4 video traces in QCIF, we run simulations to show that our proposed model estimates packet loss ratios at various traffic loads more accurately than existing modeling methods.

This paper presents the characteristics and modeling of VoIP traffic for a real network. The new model, based on measured data, shows a significant difference from the previously proposed models in terms of parameters and their effects. It is found that the effects of background noise and ringing tones have essential influences on the model. The observed distributions of talkspurt and silent durations have long-tail characteristics and considerably differ from the existing models. An additional state called "Long burst", which represents the background noise at the talker's place, is added into the continuous-time Markov process model. The other three states, "Talk", "Short silence" and "Long silence", represent the normal behavior of the VoIP user. Models for conversational speech containing the communication during the dialogue are presented. In the case of the VoIP traffic aggregation, the simplified models, which neglect the conversation's interaction, are proposed. Depending on the occurrences of background noise during the speech, the model is classified as "noisy speech" or "noiseless speech". The measured data shows that the background noise typically increases the data rate by 60%. Simulation results of aggregated VoIP traffic indicate the self-similarity, which is analogous to the measured data. Results from the measurements support the fact that except the ringing duration the conversations from both the directions can be modeled in identical manner.

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.

The problem of aggregating different stochastic process into a unique one that must be characterized based on the statistical knowledge of its components is a key point in the modeling of many complex phenomena such as the merging of traffic flows at network nodes. Depending on the physical intuition on the interaction between the processes, many different aggregation policies can be devised, from averaging to taking the maximum in each time slot. We here address flows averaging and maximum since they are very common modeling options. Then we give a set of axioms defining a general aggregation operator and, based on some advanced results of functional analysis, we investigate how the decay of correlation of the original processes affect the decay of correlation (and thus the self-similar features) of the aggregated process.

Seasonal ARIMA model is a good traffic model capable of capturing the behavior of a network traffic stream. In this paper, we give a general expression of seasonal ARIMA models with two periodicities and provide procedures to model and to predict traffic using seasonal ARIMA models. The experiments conducted in our feasibility study showed that seasonal ARIMA models can be used to model and predict actual wireless traffic such as GSM traffic in China.

Measuring and modeling network traffic is of key importance for the traffic engineering of IP networks, due to the growing diversity of multimedia applications and the need to efficiently support QoS differentiation in the network. Several recent measurements have shown that Internet traffic may incorporate long-range dependence and self-similar characteristics, which can have significant impact on network performance. Self-similar traffic shows variability over many time scales, and this behavior must be taken into account for accurate prediction of network performance. In this paper, we propose a new parameter fitting procedure for a superposition of Markov Modulated Poisson Processes (MMPPs), which is able to capture self-similarity over a range of time scales. The fitting procedure matches the complete distribution of the arrival process at each time scale of interest. We evaluate the procedure by comparing the Hurst parameter, the probability mass function at each time scale, and the queuing behavior (as assessed by the loss probability and average waiting time), corresponding to measured traffic traces and to traces synthesized according to the proposed model. We consider three measured traffic traces, all exhibiting self-similar behavior: the well-known pOct Bellcore trace, a trace of aggregated IP WAN traffic, and a trace corresponding to the popular file sharing application Kazaa. Our results show that the proposed fitting procedure is able to match closely the distribution over the time scales present in data, leading to an accurate prediction of the queuing behavior.

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.

It has been known that the cell loss ratio (CLR) characteristics of the multiplexed traffic depend on the arrangement of I-picture starting times of individual variable bit rate (VBR) MPEG video sources. In this paper, we propose a simple yet accurate traffic model for the multiplexed VBR MPEG video to calculate the CLR at an ATM multiplexer when the arrangement of the I-picture starting times of individual sources is given. In the proposed model, in order to represent the arrangement of the I-picture starting times, each picture type (I-, P-, or B-picture) of individual source is modeled by the arrival rate histogram, and the multiplexed video traffic is modeled by the convolution of the arrival rate histograms of the pictures that comprise the multiplexed traffic. Using the proposed traffic model, we propose an analytical method to calculate the CLR of the multiplexed VBR MPEG video at an ATM multiplexer. Simulation results show that the proposed method can calculate the CLR more precisely and efficiently than other existing methods.

Guarantees of quality-of-service (QoS) in the real-time transmission of video on the Internet is a challenging task for the success of many video applications. The Internet Engineering Task Force (IETF) has proposed the Guaranteed Service (GS) in the Integrated Service model with firm delay and bandwidth guarantees. For the GS, it is necessary to provide traffic sources with the capability of calculating the traffic characteristics to be declared to the network on the basis of a limited set of parameters statistically characterizing the traffic and the required level of QoS. In this paper, we develop an algorithm for the evaluation of the traffic parameters which characterize the video stream when a QoS requirement is given. To this end an analytical traffic model for the VBR MPEG video is introduced. Simulation results show that the proposed method can evaluate the traffic parameters precisely and efficiently.

It has been reported that IP packet traffic exhibits the self-similar nature and causes the degradation of network performance. Therefore it is crucial for the appropriate buffer design of routers and switches to predict the queueing behavior with self-similar input. It is well known that the fitting methods based on the second-order statistics of counts for the arrival process are not sufficient for predicting the performance of the queueing system with self-similar input. However recent studies have revealed that the loss probability of finite queuing system can be well approximated by the Markovian input models. This paper studies the time-scale impact on the loss probability of MMPP/D/1/K system where the MMPP is generated so as to match the variance of the self-similar process over specified time-scales. We investigate the loss probability in terms of system size, Hurst parameters and time-scales. We also compare the loss probability of resulting MMPP/D/1/K with simulation. Numerical results show that the loss probability of MMPP/D/1/K are not significantly affected by time-scale and that the loss probability is well approximated with resulting MMPP/D/1/K.

Two main characteristics of VBR MPEG video traffic are the different statistics according to different picture types and the periodic traffic pattern due to GOP structure. Especially, the I-pictures at the beginning of each GOP generate much more traffic than other pictures. Therefore, when several VBR MPEG video sources are superposed, the multiplexing performance can vary according to the variations of their I-picture start times. In this paper, we show how the start time arrangement of the superposed VBR MPEG videos can significantly affect the cell loss ratio characteristics at the multiplexers, by using U-NDPP/D/1/B queueing model. It is also shown that the Lognormal distribution is more suitable for modeling VBR MPEG video traffic than the Normal and Gamma distributions, in the queueing application's view points.