Long-range dependence in variable-bit-rate video traffic

It has been shown that Variable Bit Rate (VBR) video exhibits long-range dependence characteristics. Several models have been proposed to synthesize traces whose autocorrelation match that of the video traffic traces. Given the relationship between self-similarity and long- range dependence, we investigate the application of discrete-time linear scale invariant systems provided by Zhao and Rao to modeling VBR video traffic. This formulation, called a DLSI system, was derived using a continuous dilation operator in discrete-time as a direct analog of the continuous-time linear scale-invariant system formulation of Wornell and differs from other approaches such as wavelet based construction. While simulations had shown that DLSI systems were capable of generating self- similar data such as those found in network traffic, questions regarding their long-range behavior remained. Answers to these questions are dealt in this paper. We present an alternative modeling technique to model VBR video traffic using DLSI system. The proposed model has a fractional pole-zero structure and provides a good model for long-range dependent and self-similar time series. The behavioral pattern of the fractional pole-zero filter for a range of the Hurst parameter is also shown. The time-domain characteristics of the filter are analyzed using power series approximations. Comparison of output autocorrelation function (ACF) to those of the video trace ACF is made. We conclude that some samples of video data are indeed better modeled by the LSI models than the conventional models such as Markovian and Long-range dependent models.

Sensitivity analysis for output performance measures in long-range dependent queueing system

In our previous work, we proposed the TNPOSS (To Next-hop Port Sequence Switch) network which can achieve scalable fast forwarding and is suitable for delivering multimedia flows. However, TNPOSS network has no Quality of Service (QoS) tools to provide better QoS guarantee for multimedia flows which often have long-range dependence (LRD) property. To enhance the QoS ability of TNPOSS network, this paper proposes a QoS-enhanced TNPOSS (QTNPOSS) network model by introducing Fractal Leak Bucket (FLB) shaper and Weighted Fair Queuing (WFQ) scheduler into the original TNPOSS network. In the new QTNPOSS network, each packet of multimedia flows is shaped by the FLB when arriving at a node and is scheduled by the WFQ before being outputted. Based on study above, we further analyze the end-to-end (E2E) delay bound of QTNPOSS network by means of the network calculus theory which is an effective mathematical tool on analyzing the worst-case QoS performances of networks. The service curve and the formulation of E2E delay bound of QTNPOSS network are presented and proved. Extensive numerical experiments show that both the LRD property of multimedia flows and the WFQ weight have influences on the E2E delay bound, and the WFQ weight influences the E2E delay bound more greatly than the LRD property does.

Time series modeling and analysis provides means of predicting the future and has been widely used in a variety of fields ranging from seismology for predicting earthquake and volcanic eruption, to finance for risk assessment, and to quantum information processing. The conventional integer order models can only capture short-range dependence; for example, Poisson processes, Markov processes, autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) processes. In time series analysis, one of the conventional assumptions is that the coupling between values at different time instants decreases rapidly as the time difference or distance increases. However, there are situations where strong coupling between values at different times exhibit properties of long range dependence which cannot be processed by the conventional time series analysis. Typical examples of long range dependence signals include financial time series, underwater noise, electroencephalography (EEG) signal, etc. ARFIMA, a fractional order signal processing technique, is the generalization of the conventional integer order techniques, namely, ARIMA and ARMA methods. Hence, it is capable of capturing both short-range dependence and long-range dependence in signals. Compared to conventional integer order models, the ARFIMA model gives a better fit and result when dealing with the data which possess the long range dependence property. In this paper, we investigate the application of the ARFIMA as well as AR methods to model EEG signals obtained from different brain channels. We analyze the resulting correlations for comparison the benefits of ARFIMA over AR on the EEG data exhibiting the long range dependency property. The results showed that the prediction results have a better performance compared to the conventional ARMA models.

On the origins of long-range dependence in TCP traffic

The Shape of the Loss Curve and the Impact of Long-Range Dependence on Network Performance

Recent studies and traffic measurements have shown that variable bit rate (VBR) video traffic, as well as local area network (LAN) traffic, exhibits long-range dependence (LRD). When this kind of traffic is transmitted over ATM networks, the LRD property implies a larger requirement in buffer allocation and channel capacity. A new fractional ARIMA model for VBR MPEG video traffic at frame level is presented. The fractional integrative component of the model is based on a process called "fractional differencing". The model is obtained from three very long sequences. It is used to synthesize artificial traffic, which presents the desired LRD.

Long-range dependent (LRD) phenomena were first exhibited by Hurst for hydrology purposes. This phenomenon occurs from the superposition of independent sources, e.g. confluent rivers provide this behaviour (see Fig. 4.2). Such aggregation procedures provide this new phenomenon. Hurst (Trans Am Soc Civ Eng 116:770–799, 1951) originally determined the optimum dam sizing for the Nile river’s volatile rain and drought conditions observed over a long period of time. LRD is characterized by slow decorrelation properties and the behaviour of partial sums’s variances. This phenomenon is discussed above, see Sects. 4.3 and 4.4. Asymptotic properties of instantaneous functions of Gaussian processes are provided in Remark 5.2.4. Infinite moving averages models with LRD properties are provided in Sects. 6.4 and 6.6. We refer the reader to Doukhan et al. (Theory and applications of long-range dependence. Birkhauser, Boston, 2002b) for much more.

We investigate transport layer processing intended to improve the communication of multimedia data over wireless and wireline networks. Specifically, we consider data striping and thinning techniques, which are applicable to the multipath/multiflow transmission of multimedia (e.g., MPEG-4). We also introduce the shuffling procedure, which reorders the data at the network edges. We show that all three techniques break up short-term correlations in data traffic thus improving its queueing performance. We demonstrate that while both long range dependence (LRD) and short range dependence (SRD) influence the queueing performance for some timescale of the queueing system, it is the short-range statistical properties of multimedia traffic within the critical time scale that are dominant in determining the buffer efficiency of the queue. We also show that estimation of LRD for thinned and striped data may lead to a misleading notion of LRD reduction, when none is warranted. We further outline the ideas for a new transport layer protocol that explores the combination of thinning, striping and shuffling approaches to multimedia data transmission.

In this paper, we propose a fractional stochastic volatility jump-diffusion model which extends the Bates(1996) model. Where we model the volatility as a fractional process. Extensive empirical studies show that the distributions of the logarithmic returns of financial asset usually exhibit properties of self-similarity and long-range dependence and since the fractional Brownian motion has these two important properties, it has the ability to capture the behavior of underlying asset price. Further incorporating jumps into the stochastic volatility framework gives further freedom to financial mathematicians to fit both the short and long end of the implied volatility surface. We propose a stochastic model which contains both fractional and jump process. Then we price options using Monte Carlo simulations along with a variance reduction technique(antithetic variates). We use market data from the S&P 500 index and we compare our results with the Heston and Bates model using error measures. The results show our model greatly outperforms previous models in terms of estimation accuracy.

The burstiness and long-range dependence constitutes important characteristics of high-speed communication network traffic, which have been extensively studied in the past decade. Though several existing models can account for the long-range dependence, the burstiness has not been captured as well. In this paper, we propose a truncated α-stable longrange dependent process model (TSLRDP), which incorporates the long-range dependence and burstiness precisely into one model. Furthermore, it demonstrates considerable flexibility in adapting real traffic. A novel algorithmic procedure to estimate the model parameters from real traffic is presented. Simulation results show that the proposed TSLRDP model fits the real traffic accurately.

A packet switched network such as the Internet provides only the best-effort service for users. Recent studies of the characteristics of packet arrival on a packet switched network have shown a self-similar property with long-range dependence, and also show a heavy-tailed distribution. This paper investigates end-to-end performance of the Internet empirically. It focuses on the inter-arrival process of packets and the property of packet loss between end-to-end hosts. We show that both the inter-arrival process and loss events are self-similar with a long-range dependence property. The inter-arrival process of packets has a heavy-tailed distribution which sums up the difference of all queues in intermediate routers.

There is mounting experimental evidence that network traffic processes exhibit ubiquitous properties of self-similarity and long range dependence (LRD), i.e. of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much recent modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the first-order statistics such as the marginal distribution of the process.We introduce and evaluate a model in which these parameters can be easily controlled. Specifically, our model is a modulated fluid traffic model in which the correlation function of the fluid rate is asymptotically second-order self-similar with given Hurst parameter, then drops to zero at a cutoff time lag. We develop a very efficient numerical procedure to evaluate the performance of the single server queue fed with the above fluid input process. We use this procedure to examine the fluid loss rate for a wide range of marginal distributions, Hurst parameters, cutoff lags, and buffer sizes.Our main results are as follows. First, we find that the amount of correlation that needs to be taken into account for performance evaluation depends not only on the correlation structure of the source traffic, but also on time scales specific to the system under study. For example, the time scale associated to a queueing system is a function of the maximum buffer size. Thus for finite buffer queues, we find that the impact on loss of the correlation in the arrival process becomes nil beyond a time scale we refer to as the correlation horizon. Second, we find that loss depends in a crucial way on the marginal distribution of the fluid rate process. Third, our results suggest that reducing loss by buffering is hard. We advocate the use of source traffic control and statistical multiplexing instead.

Reservation arbitrated access — a bandwidth on demand protocol for multiplexing variable bit rate isochronous traffic over dual bus metropolitan area networks

MPEG video traffic is expected to represent most of the load in the future high-speed networks. Adequate traffic models for MPEG Variable Bit-Rate (VBR) video are important for network design, performance evaluation, admission control and resource allocation.It is well-known that VBR video exhibits long-range correlations over arbitrarily long time-scales, a phenomenon usually referred to as Long-Range Dependence (LRD).Many models for VBR video traffic have been proposed in the literature. However, while the correlation between Groups of Pictures (GOPs) has been widely analyzed in literature, little effort has been devoted up to now to the generation of the different frame-types within a MPEG GOP.Due to the difficulty and complexity involved in this issue, this is often neglected even though it is a fundamental characteristic of MPEG traffic and it might have an important impact on queueing performance. In fact, many works avoid to descend to the frame level proposing models for the GOP process.In this paper, we analyze the impact on queueing performance of different solutions proposed in the literature for generating the different types of MPEG frames within a GOP (these solutions have never been compared and analyzed jointly). In this way, we can be in a good position to use the best model for MPEG in terms of simplicity, computational efficiency and queueing performance, depending on the performance metric to study (loss rate, mean delay and jitter).