W.-C. Lau, A. Erramilli, J. Wang, and W. Willinger, "Self-similar traffic generation: The random midpoint displacement algorithm and its properties," in IEEE Int. Conf. on Comm., pp. 466--472, June 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the theoretical network bandwidth utilization is equal to 0.73. In this simulation the TDMA frame length is set to 27 ms and each frame consists of 32 satellite channel bursts. The traffic generators at the ports of the terminals are modeled using a self similar traffic model as described in [2]. Further model coding optimization has been performed which resulted in a more efficient self similar traffic generator. The model requires three input parameters: the mean traffic m, the normalized standard deviation a, and the Hurst parameter H.Forthe simulation the value of a is set to 1.0 ....

Lau, W-C., et al, "Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties", Proceedings of the IEEE ICC'95, pp. 466-472.

....showed in [6] that this Gaussian convergence does occur. Figure 1 shows members of a family of M Pareto processes, all with the same values of m, oe 2 and H , but with differing levels of aggregation. Also shown is the performance of a Gaussian process, simulated using the technique described in [13], also with the same values of m, oe 2 and H . As the value of increases, the queueing performance of the M Pareto improves, until a good approximation of Gaussian performance is achieved. Along the way, however, lower values of produce quite different results, even 0.001 0.01 0.1 1 0 50 ....

W. Lau, A. Erramilli, J. L. Wang, and W. Willinger. Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and its Properties. In Proceedings of ICC '95, 1995.

....V and H as functions of up and down link attenuations The method followed does not rigorously give an indication as to the self affine nature of the process, nor does it give a precise estimation of the Hurst parameter. Other methods are commonly used to estimate the Hurst parameter of a process [6, 7], one of which can be used to compute confidence intervals. All these methods also give an idea of whether the process being measured can be considered to be self affine. In order to get such information, an analysis of the process that spans several decades of time scales is required, while we ....

....and that its s 2 and its fractal dimension (hence the Hurst parameter) are locally the same as those of the measured attenuation. Of the various methods available for generating fBm, many of which are dealt with in [3, 4] we chose the random midpoint displacement algorithm, rmd for short [6]. It is much simpler and quicker than the other methods, though it is only an approximation of a real fBm process. Despite this, rmd is sufficient for most uses. In [6] the authors show that an acceptable degree of precision is achieved as far as the target value of H is concerned, unless H is ....

[Article contains additional citation context not shown here]

Lau, Erramilli, Wang, Willinger, "Self-similar traffic generation: the random midpoint displacement algorithm and its properties", Int. Conf. on Communications, June 1995, Seattle, USA, 466-472.

....limit theorem, the Gaussian model accurately represents aggregation of many traffic streams. This has been proved in [4] and is illustrated by simulation in Section 5. Fractional Brownian Noise traces used in the simulations described in this paper were generated by the technique described in [8]. 4.1 The Discrete Gaussian Model Consider a FIFO single server queue, let time be divided into fixed length sampling intervals. and consider all the definitions and notation of the discrete time queueueing model described in Section 2.3. we now suppose that the arrival process, namely the fA n ....

W. Lau, A. Erramilli, J. L. Wang, and W. Willinger. Self-similar traffic generation: The random midpoint displacement algorithm and its properties. In Proceedings of ICC 95, 1995.

....between the degree of self similarity and the length of computation. Random Midpoint Displacement (RDM) method Given that the exact generation of fBm traces is practically infeasible (due to the large amount of required CPU time) a more efficient approximate algorithm is the RMD method [23]. A self similar process can be synthesized by progressively subdividing an interval over which a sample path is generated at the midpoint from the values at the endpoints. At each division, a zero mean Gaussian displacement is used to determine the value of the sample path at the midpoint of the ....

Lau W.C., Erramilli A., Wang J.L. and Willinger W., Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties, Proceedings of IEEE ICC'95, 1995.

....for higher frequencies. 2 0 2 4 6 8 0 2 4 6 8 10 12 14 16 18 m H=0.75 with Daubechies Bases with N=2. 11 Fig. 1. Hurst estimation for a fGn sample path with different wavelet bases As shown in [14] in case of fGn sequences (generated using the Random Midpoint Displacement algorithm [15]) the wavelet approach is more efficient than traditional estimation methods and it works with relatively short traces (the deviation from the nominal value is lower than 2 even with a few thousands of samples) 5 Wavelet Analysis of Self Similar Traffic Processes The wavelet approach can be ....

Lau W.C., Erramilli A., Wang J.L., and Willinger W. Self-similar traffic generation: The random midpoint displacement algorithm and its properties. In Proceedings of IEEE ICC 95, pages 466--472, Seattle, June 1995.

....the queue both with FGN paths and with synthetic traces, generated on the basis of an actual one. Since we resort to IS, we can extend the comparison up to very low buffer occupancy probabilities. In order to generate FGN traces we used a method based on the Random Midpoint Displacement Algorithm [11]. The choice was mainly due to the fact that this algorithm does not require a great computational effort and this property makes it particularly attractive for simulations. The modeling procedure used to approximate real traffic follows the one proposed for VBR video in [9] based on the fitting ....

W.-C. Lau, A. Erramilli, J. L. Wang and W. Willinger. "Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and its Properties". In Proc. of the ICC '95, pages 466-472, Seattle, WA, 1995.

.... been widely investigated in literature and are considered among the most realistic traffic models in the field of broadband networks [10] The adopted generation procedure is the well known Random Midpoint Displacement (RMD) algorithm, designed to accurately and quickly generate long fGn traces [7]. IV Wavelet Estimation of the Hurst parameter Since the Wavelet Transform implies the decomposition of a signal at different resolutions and the mother wavelet itself is defined recursively, it appears as the natural tool for the analysis of selfsimilar processes, which present the same ....

Lau W.C., Erramilli A., Wang J.L., Willinger W., "Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and its properties", ICC' 95, pp. 466-472, Seattle, 1995

....the traces is a lower height of the peaks in the bytes vs. time plot. Considering the particular structure of the data pattern it is interesting to compare the proposed model with a more traditional self similar process, such as a fGn produced by a Random Midpoint Displacement generator (RMD) [6]. The synthetic trace generated by the RMD model presents high burstiness but does not capture the evident difference between high and low activity levels. Considering just their self similar analysis the data present the same statistical behaviour. Figures 4.2 shows a comparison among the three ....

W.Lau,A.Erramilli, J.J.Wang, W.Willinger "Self similar traffic generation: The random midpoint displacement algorithm and its properties" IEEE ICC `95 Seattle

....that any direct FFT based synthesis of sampled fBm through this approach is undesirable because the same sampling and smearing effects occur. Moreover, any process synthesized by this approach will be stationary, whereas fBm is nonstationary. 2.4. 3 Random midpoint displacement The next technique [29] synthesizes the values of a sampled fBm trace at a few dispersed points and then successively refines (or randomly interpolates) the values between the synthesized points. 12 Since it does not attempt to model all cross covariances between all fBm samples, it is inexact and in practice can ....

W.-C. Lau, A. Erramilli, J. Wang, and W. Willinger, "Self-similar traffic generation: The random midpoint displacement algorithm and its properties," in IEEE Int. Conf. on Comm., pp. 466--472, June 1995.

....traffic and for each source. The latter analysis has been carried out in order to test the fairness of the analysed scheduling algorithm. The data traffic used to drive simulations was both the acquired data and synthetic FGN traces generated with the Random Midpoint Displacement (RMD) algorithm [9]. This method permits to generate selfsimilar sample paths with determined value of mean, variance and Hurst parameter, which completely characterise the FGN process. In more details simulations have been conducted under the following working conditions: each input trace represents the number ....

W. C. Lau, A. Erramilli, J. L. Wang, W. Willinger "Self-similar traffic generation: the Random Midpoint Displacement algorithm and its properties" Proc of the ICC '95, pages 466-472, Seattle, WA, 1995

....how to incorporate self similarity into the traffic models used in a simulation. Accurate synthesis of aggregate self similar traffic remains an open problem. A number of algorithms exist for synthesizing exact or approximate sample paths for different forms of self similar processes [GW94, LEWW95, Pax97b, RL95, Fla92] These, however, solve only one part of the problem, namely how to generate a specific instance of a set of longer term traffic correlations. The next step how to go from the pure correlational structure, expressed in terms of a time series of packet arrivals per unit ....

W-C. Lau, A. Erramilli, J. Wang, and W. Willinger, "Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties," Proceedings of ICC '95, 1995.

....which can be seen in figure 10. The self similar cell stream generator we want to introduce, is based on a standard C portation of the Fractional Gaussian Noise (FGN) generator described in [9] It is one of the fastest known methods and rather easy to implement compared to other algotithms [2,5,7]. While the original program generates a sequence of positive and negative real values, we face the problem of converting these values to appropriate cell count values without destroying the self similar properties. An unresolved problem in this context is the actual bandwith distribution of real ....

W-C. Lau, A. Erramilli, J. Wang, W. Willinger, "Self-Similar Traffic Generation: The Random Midpoint Replacement Algorithm and It's Properties", ICC `95, 1995

....a lower value models a video source with low complexity. Finally, the mean of the process is increased by a m value. With this value there is the possibility of modeling different qualities of the MPEG codification. F ARIMA D m Synth. traffic Fig. 10. VBR video traffic generation In [11] and [12], two previous models to generate long range dependence have been presented. The first one deals with the Hosking s algorithm. The main disadvantage of this model is the need of storing all the previous samples in to generate a new one. Thus, this algorithm needs a large and variable amount of ....

....However, the model presented in this work needs a little and constant amount of memory. The time wasted to generate every new sample is constant and negligible. Thus, it can be used to drive simulations on real time . On the other hand, the random midpoint displacement algorithm is presented in [12]. Nevertheless, this algorithm can not be used to synthesize traffic on line for driving simulations, because it must generate the complete set of samples before the generated traffic can be used. 6. Conclusions The self similar nature of the VBR MPEG video traffic has been shown in several ....

W.C. Lau, A. Erramilli, J. L. Wang and W. Willinger, "Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties", Proceedings of IEEE INFOCOM'95, pp.466-472, 1995.

.... such results were due to inherent self similarity within the data and secondly those who suggested the results were merely a manifestation of the nonstationary nature of such traces [3] The present consensus seems to be that self similar models generate traffic streams that match the data well [4] and hence work under the premise that if the model fits it is a good model. Whether this goodness of fit is due to the data being self similar, nonstationary or a mixture of both is still unclear. If Ethernet traces are inherently self similar then several problems arise: ffl The developing ....

W. C. Lau, A. Erramilli, J. L Wang, and W. Willinger. Self-similar traffic generation: The random midpoint displacement algorithm and its properties. In Proceedings of ICC 1995, pages 466--472, 1995.

....The drawback of a method based on this observation is that the process is only asymptotically self similar, so again one must trade off length of computation for degree of self similarity. ffl A third method of synthesizing a self similar process is the Random Midpoint Displacement (RMD) method [LEWW95], which works by progressively subdividing an interval over which to generate the sample path. At each division, a Gaussian displacement is used to determine the value of the sample path at the midpoint of the subinterval. Self similarity comes about by appropriate scaling of the variance of this ....

.... tasks the S interpreter runs about twice as fast on a SPARCstation 20 as on the IPX model, so comparing these timings with those for the RMD method given in x 2 indicates that our implementation of the FFT method runs more than twice as fast as the implementation of the RMD method used by [LEWW95]. It could easily be that the RMD method (or the FFT method) can be sped up further by some hand tuning; however, the general conclusion that the FFT method runs quite quickly and is comparable in efficiency with the RMD method seems clear. We then assessed how well samples produced by the method ....

[Article contains additional citation context not shown here]

W-C. Lau, A. Erramilli, J. Wang, and W. Willinger, "Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties," Proceedings of ICC '95, 1995.

....have been applied in variablebit rate (VBR) video (Beran et at. 22] Garrett and Willinger [26] Huang et al. 29] and McLaren and Nguyen [38] LAN traffic Chen et al. 24] Dueck [25] and Leland et al. 34] 35] traffic generation (Garrett and Willinger [26] Huang et al. 28] Lau et al. [33]) progressive image coding for packet switching communications (Carlini et al. 23] and estimation from noisy data (Kaplan and Kuo [30] Another approach suitable for modeling VBR video is based on TES models (Lee [46] Melamed et al. 47] 49] Lambadaris et al. 45] This approach takes ....

W. Lau, A. Erramilli, J. Wang, and W. Willinger, "Self-similar traffic generation: The random midpoint displacement algorithm and its properties", in Proc. IEEE Int Conf. Commun., 1995.

....P ( 1 as 0. The significance of long range dependencies were recently identified in real traffic measurement [14] Due to the absence of queueing techniques with self similar arrival processes, queueing solutions have to rely on simulations with synthetically generated traces [13] [15]. Yet, none of the approximate methods for generating long traces within a reasonable amount of time are well understood regarding their accuracy and quality [15] The impact of traffic long term dependencies on queues will not be the subject of this study, although it is possible to design a ....

.... with self similar arrival processes, queueing solutions have to rely on simulations with synthetically generated traces [13] 15] Yet, none of the approximate methods for generating long traces within a reasonable amount of time are well understood regarding their accuracy and quality [15]. The impact of traffic long term dependencies on queues will not be the subject of this study, although it is possible to design a large state space Markov model or a high order autoregressive model to approximately characterize the fractal property [2] 1.1 Related Works To the best of our ....

W. Lau, Ashok Erramilli, J. Wang, and W. Willinger, "Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties," Proc. of ICC'95, 1995, pp. 466-472.

....In the absence of methods that can permit the routine analysis of fractal queueing systems, simulation methods are suggested for routine analysis. The generation and statistical analysis of traffic with long range dependence heavy tails is an active area of current research (see for example [14], 27] 28] 10] 24] There are nevertheless several analytical results which provide considerable insights into the engineering impacts of fractal traffic. These are discussed next. IV. Engineering Impacts In this section, we will briefly review current insights into the performance and ....

W.-C. Lau, A. Erramilli, J.L. Wang and W. Willinger. SelfSimilar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties. Proc. of the ICC'95 , Seattle, WA, On the self-similar nature of Ethernet traffic. ACM/SIGCOMM Computer Communications Review, Vol. 23, pp. 183--193,

....practice. There exist numerous methods to date for generating self similar traffic traces. Exact methods, which are based on the Durbin Levinson algorithm [37, 394] are discussed in [24, 146, 196, 198, 394] They are generally impractical for long time series. Approximate methods are described in [30, 74, 120, 215, 245, 252, 258, 285, 290, 331, 334, 337, 356, 374, 376, 404,412]; some of these methods rely on earlier results reported in [77, 165,391] derived for a different purpose and re interpreted here in the context of synthetic traffic generation. These methods are generally very fast and feasible for even A Bibliographical Guide 7 very long time series. However, ....

....a different purpose and re interpreted here in the context of synthetic traffic generation. These methods are generally very fast and feasible for even A Bibliographical Guide 7 very long time series. However, the statistical quality of the generated sequences is, in general, not well understood [252]. Acknowledgment. This work was partially supported by the NSF Grants DMS9404093 and NCR 9404931 at Boston University. ....

W.-C. Lau, A. Erramilli, J. L. Wang, and W. Willinger. Self-similar traffic generation: The random midpoint displacement algorithm and its properties. In Proceedings of the ICC '95, pages 466--472, Seattle, WA, 1995. A Bibliographical Guide 23

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W.-C. Lau, A. Erramilli, J. Wang, and W. Willinger, "Self-similar traffic generation: The random midpoint displacement algorithm and its properties," in IEEE Int. Conf. on Comm., pp. 466--472, June 1995.

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W. Lau, Ashok Erramilli, J. Wang, and W. Willinger, "Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties," Submitted for publication.

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Wing-Cheong Lau, Ashok Erramilli, Jonathan L.Wang, Walter Willinger "Self-Similar Traffic Generation: The Random Midpoint displacement Algorithm and Its Properties", ICC '95, Seattle, Washington USA, June 18-22 1995, pp. 466-472.

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W.-C. Lau, A. Erramilli, J. L. Wang, and W. Willinger. Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and its Properties. In Proceedings of the IEEE ICC, 466--472, 1995. (p 39)

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W. Lau, A. Erramilli, J. Wang, and W. Willinger, "Self-Similar traffic generation: the random midpoint displacement algorithm and its properties, " Proc. ICC '95, 1995.

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