Performance of finite-buffer queues under traffic with long-range dependence

The objective of this paper is to demonstrate the limitations of the variance-time (VT) test as a statistical tool for inferring long-range dependence (LRD) in network traffic. Since the early Bellcore studies, LRD has been in the center of a continuous debate within the teletraffic community. The controversy is typically focused on the utility of LRD models to predict the performance at network buffers. Our work here is not meant to advocate one modeling approach over another, but to point out (experimentally and theoretically) to the caveats in using the VT test as a tool for detecting LRD. We do that by deriving simple analytical expressions for the slope of the aggregated variance in three autocorrelated traffic models: M/G//spl infin/ process (short-range dependent (SRD) but non-Markovian), the discrete autoregressive of order one model (SRD Markovian), and the fractional ARIMA process (LRD). Our main result is that the VT test often indicates, falsely, the existence of an LRD structure (i.e., H>0.5) in synthetically generated traces from the two SRD models. The bias in the VT test, however, diminishes monotonically with the length of the trace. We provide some guidelines on selecting the minimum trace length so that the bias is negligible.

The paper deals with the applicability of fractional AutoRegressive Integrated Moving Average (f-ARIMA) processes to traffic modelling. This study is suggested by the ability of f-ARIMA processes in separately capturing both the long range dependence (LRD) and short range dependence (SRD) features of actual traffic. Indeed, the f-ARIMA models permit one to produce synthetic traces with a well-controlled LRD/SRD component ratio. The practical relevance of this feature is tested analytically, by means of discrete event simulations, the queueing performance in several working conditions for two different actual-traffic data sets, respectively related to a LAN-to-LAN interconnection and a videoconference service. In particular, the latter data set, characterised by a strong low frequency SRD component, emphasises the improvement on queueing performance evaluation introduced by a low-order f-ARIMA (p,d,0) model with respect to a pure LRD one. On the contrary, the inadequacy of the f-ARIMA model is highlighted when considering the LAN traffic characterised by a quite complex SRD component.

Heavy traffic analysis for a multiplexer driven by M∨GI∨∞ input processes

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.

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.

Network study finds simultaneous presentation of long-range dependence and short-range dependence in Network traffic., which makes the performance of the traditional model used to describe the short-range dependence for prediction lower. And in different scales of these two characteristics of network traffic have different impact for network performance. In small enough scale the short-range dependence has a greater impact on network performance, while in large enough scale, long-range dependence characteristics play a leading role. Therefore, in order to obtain better prediction this paper makes network traffic sequence more smooth and easy to be fitted by the traditional model, through weakening the dependence not affording a major role in small scale and enhancing the dependence playing a leading role in the impact of network.

Markov-modulated Poisson process (MMPP) is one of the popular non-self-similar schemes for modeling network traffic. They are used for modeling both short-range dependent (SRD) and long-range dependent (LRD) traffic. The paper verifies Algorithm LAMBDA for fitting MMPP to synthetic traffic and evaluates the accuracy of the fitted MMPP model. We provide evidence that, for self-similar traffic, the performance highly depends on Hurst parameter. In some cases, the algorithm exhibits some inaccuracy in mean queuing delays. We try to modify it by a simple change in order to make the algorithm adaptive, and consequently, make the results more realistic.

Network traffic exhibits fractal properties, such as self- similarity and impulsiveness, and posseses a complex correlation structure, i. e., both long and short-range dependence are present. Models such as Fractional Gaussian Noise can capture the long-range dependence but not the short-range dependence. Therefore, a key issue that must be adressed when using synthesized traffic for network simulations is the incorporation of short-range dependence into the generated trace. This work develops a filter-based method for the introduction of short- range dependence into long-range dependent sample paths that are synthesized via wavelets and studies a method of mapping from a given time series to a packet stream. The generator does not employ training sequences, i. e., it is not based on the use of real traffic traces as training sequences.

Accurate modeling of VoIP traffic QoS parameters in current and future networks with multifractal and Markov models

Due to the strong experimental evidence that the traffic to be offered to future broadband networks will display long-range dependence, it is important to study the possible implications that such traffic models may have for the design and performance of these networks. In this paper we consider the popular leaky bucket flow control scheme with long-range dependent input traffic, which is a generalization of the model for long-range dependent traffic suggested in Likhanov et al. (1995). We prove that the departure process of the leaky bucket policing mechanism driven by such an arrival process is long-range dependent for any token buffer size and any -finite or infinite-cell buffer size.

Most of the proposed self-similar traffic models are asymptotic in nature. Hence, they are less effective in queueing-based performance evaluation when the buffer sizes are small. In this paper, we propose a short range dependent (SRD) process modelling by a generalized variance-based Markovian fitting to provide effective queueing-based performance measures when buffer sizes are small. The proposed method is to match the variance of the exact second-order self-similar processes. The fitting procedure determines the related parameters in an exact and straightforward way. The resultant traffic model essentially consists of a superposition of several two-state Markov-modulated Poisson processes (MMPPs) with distinct modulating parameters. We present how well the resultant MMPP could emulate the variance of original self-similar traffic in the range of the specified time scale, and could provide more accurate bounds for the queueing-based performance measures, namely tail probability, mean waiting time and loss probability. Numerical results show that both the second-order statistics and queueing-based performance measures when buffer capacity is small are more accurate than that of the variance-based fitting where the modulating parameters of each superposed two-state MMPP are equal. We then investigate the relationship between time scale and the number of superposed two-state MMPPs. We found that when the performance measures pertaining to larger time scales are not better than that of smaller ones, we need to increase the number of superposed two-state MMPPs to maintain the accurate and reliable queueing-based performance measures. We then conclude from the extensive numerical examples that an exact second-order self-similar traffic can be well represented by the proposed model.

Long-range dependence has been recently asserted to be an important characteristic in modeling telecommunications traffic. Inspired by the integral relationship between the fractional Brownian motion and the standard Brownian motion, we model a process with long-range dependence, Y, as a fractional integral of Riemann-Liouville type applied to a more standard process X—one that does not have long-range dependence. When X takes the form of a sample path process with bounded stationary increments, we provide a criterion for X to satisfy a moderate deviations principle (MDP). Based on the MDP of X, we then establish the MDP for Y. Furthermore, we characterize, in terms of the MDP, the transient behavior of queues when fed with the long-range dependent input process Y. In particular, we identify the most likely path that leads to a large queue, and demonstrate that unlike the case where the input has short-range dependence, the path here is nonlinear.

Accurate evaluation of the long-range dependence in hydroclimatic time series is important for understanding its inherent characteristics. However, the reliability of its evaluation may be questioned, since different methods may yield various outcomes. In this study, we evaluate the performances of seven widely used methods for estimating long-range dependence: absolute moment estimation, difference variance estimation, residuals variance estimation, rescaled range estimation, periodogram estimation, wavelet estimation (WLE), and discrete second derivative estimation (DSDE). We examine the influences of six major factors: data length, mean value, three nonstationary components (trend, jump, and periodicity), and one stationary component (short-range dependence). Results from the Monte Carlo experiments show that WLE and DSDE have greater credibility than the other five methods. They also reveal that data length, as well as stationary and nonstationary components, have notable influences on the evaluation of long-range dependence. Following it, we use the WLE and DSDE methods to evaluate the long-range dependence of precipitation during 1961–2015 on the Tibetan Plateau. The results indicate that the precipitation variability mirrors the long-range dependence of the Indian summer monsoon but with obvious spatial difference. This result is consistent with the observations made by previous studies, further confirming the superiority of the WLE and DSDE methods. The outcomes from this study have important implications for modeling and prediction of hydroclimatic time series.

This paper presents a new MPEG-4 video traffic model, which efficiently exploits the frame pattern of MPEG-4 video by using IBB and PBB sequences as the basic units and modeling their dependence in the orthogonal domain after Hadamard transform. This model can accurately capture both short range dependence (SRD) and long range dependence (LRD) characteristics of MPEG-4 video data. Simulation results demonstrate that the probability density function and the autocorrelation function of model data are highly close to those of real data. And in the leaky bucket performance test, using the model data as input source obtains almost the same estimates of the required buffer size or bit loss rate as using real data. Furthermore, our new model needs very few parameters and has high computational efficiency, thus is very suitable to be used as the video source in the study such as cellular network design and evaluation, wireless resource management and so on.

Quality of Service (QoS) and queue management are important issues for IEEE 802.11 systems. However, existing 2-dimensional (2-D) Markov chain models of 802.11 systems are unable to capture the complete QoS performance and queueing behavior due to the lack of an adequate finite buffer model. We present a 3-dimensional (3-D) Markov chain that integrates the 802.11 system contention resolution and queueing processes into one model. The 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> dimension, that models the queue length, allows us to accurately capture important QoS measures, delay and loss, plus throughput and queue length, for realistic 802.11 systems with finite buffer under finite load. We derive an efficient method for solving the steady state probabilities of the Markov chain. Our 3-D Markov chain is the first finite buffer model defined and solved for 802.11 systems. The solutions, validated by extensive simulations, capture the system dynamics over a wide range of traffic load, buffer capacity, and network size. Our 3-D model points to the existence of an effective maximum throughput and shows its relationship with buffer capacity. We demonstrate that our 3-D model can also be used in resource allocation to determine adequate buffer sizes under a particular QoS constraint.