Robert, S. and Le Boudec, J. (1997). New models for pseudo self-similar traffic. Performance Evaluation, 30(1--2):57--68.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of a large number of techniques and tools for computing performance measures for systems underlying such a workload. In this paper, after a brief introduction to self similarity in Section 2, we focus on the so called pseudo selfsimilar traffic (PSST) model, as introduced by Robert and Le Boudec [35, 36], in Section 3. This model is both simple and intuitively appealing, however, when applying this model in a number of cases, we have encountered various shortcomings, on which we report in Section 4. We then show that these shortcomings are not specific to our case studies, but instead that they ....

....derive oqp=r 46587 s o6ptr e3kuh o6ptr 9 so that h emerges as the negative gradient in the above mentioned plot. Using a linear regression technique on this plot, we can estimate and, hence, 3. The pseudo self similar traffic model We describe the PSST model, as introduced in [35, 36], in Section 3.1 and discuss the computation of its parameters in Section 3.2. A continuous time variant of the model is presented in Section 3.3 3.1. Model definition Model description. The PSST model attempts to characterise traffic self similarity by the use of a discrete time Markov ....

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S. Robert and J.-Y. Le Boudec. New models for pseudo self-similar traffic. Performance Evaluation, 30:57--68, 1997.

....use the name of local Hurst H l parameter instead of Hurst parameter for our Markov chains. The Markov chains we examine have pseudo long range dependences. The self similarity tests performed on these chains (by the variances method and the visual test) and the fitting problem can be found in [21]. 3.2 Validation on a queuing problem Here, we consider an ATM link buffer; the process of cell arrivals on a slotted link. The service time is equal to one slot and can only start at the beginning of a slot. No priority level is considered here and the service strategy of the queue is First In ....

S. Robert and J.-Y. L. Boudec, "New Models for Pseudo Self-Similar Traffic," to appear in Performance Evaluation, 1996.

....of traffic processes. Such approaches include chaotic maps [5] a LRD ON OFF model [18] Cox s M G 1 type models [4,8,11,17] the Fractional Brownian motion (FBm) model [9,10] fractional autoregressive integrated moving average (FARIMA) models [7,15] point processes [14] and pseudo models [1,13]. An issue of much interest is whether and how multifractal can be employed to model LRD traffic. Recently Taqqu et al. 16] have analyzed aggregated network traffic processes using the multifractal concept. They conclude that when selfsimilar traffic models can be applied, multifractal models may ....

S. Robert and J.-Y. Boudec, 1997: New models for pseudo self-similar traffic. Performance Evaluation, 30 57--68.

....of traffic processes. Such approaches include chaotic maps [5] a LRD ON OFF model [20] Cox s M G 1 type models [4,10,13,19] the Fractional Brownian motion (FBm) model [11,12] fractional autoregressive integrated moving average (FARIMA) models [9,17] point processes [16] and pseudo models [1,15]. An issue of much interest is whether and how multifractal can be employed to model LRD traffic. Using Bellcore s LAN and WAN traffic trace data, we have found [7] that the interarrival time series and the packet length sequences are long range dependent, and are multifractals over certain ....

S. Robert and J.-Y. Boudec, 1997: New models for pseudo self-similar traffic. Performance Evaluation, 30 57--68.

....into the relation between the power tail distributions parameters and the queueing performance measures. In order to obtain more quantitative results, several contributions have recently suggested to fit hyperexponential distributions, i. e, mixture of exponentials, to power tail distributions [9,12,20] (see also the related work [2,21] However, none of the fitting algorithms developed in these work provide a systematic way for deriving an approximation arbitrarily close to the original distribution. Moreover, the queueing results obtained via these approaches are only numerical. Inspired by a ....

....deriving an hyperexponential distribution is simply to divide (15) by (16) A potential drawback of this approach is that the inaccuracy resulting from the truncation of high frequencies may have an impact on the quality of the approximation for large values of t. Using the same terminology as [20], we refer to G(t) as a pseudo Pareto distribution. Of course, the pseudo Pareto distribution can be made arbitrarily 10 Starobinski and Sidi Modeling and Analysis of Power Tail Distributions close to the exact Pareto distribution by letting B 1, N 1 and M Gamma1. As an illustration ....

S. Robert and J.-Y. Le Boudec, New Models for Pseudo Self-Similar Traffic, Performance Evaluation, Vol.30, pp.57-68, 1997.

....a mixture of exponential distributions. Hyperexponential distributions are easier to analyze since they have explicit rational Laplace transforms. In fact, several contributions have recently proposed heuristic algorithms for fitting hyperexponential distributions to heavy tailed distributions [FeW98, GJL99, RoL97] (see also the related work [AnN98] However, none of the fitting algorithms developed in these works provide a systematic way for deriving an approximation arbitrarily close to the original distribution. Moreover, the queueing results obtained via these approaches are only numerical. Inspired by ....

....exp( GammaB Gamman ) exp( GammaaB Gamman t) 2.19) For large values of B, it may happen that is larger than 1 (due to the discretization error) In such a case, the value of M must be appropriately increased in order to ensure that is smaller than 1. Using the same terminology as [RoL97], we refer to G(t) as a pseudo Pareto distribution. Of course, the pseudo Pareto distribution can be made arbitrarily close to the exact Pareto distribution by letting B 1, N 1 and M Gamma1. As an illustration of the fitting method, a Pareto distribution with ccdf F (t) 1= 1 0:5 ....

S. Robert and J.-Y. Le Boudec "New Models for Pseudo Self-Similar Traffic," Performance Evaluation, Vol.30, pp.57-68, 1997.

....into the relation between the heavy tailed distributions parameters and the queueing performance measures. In order to obtain more quantitative results, several contributions have recently suggested to fit hyperexponential distributions, i. e, mixture of exponentials, to heavy tailed distributions [FeW98, 1 GJL99, RoL97] (see also the related work [AnN98] However, none of the fitting algorithms developed in these works provide a systematic way for deriving an approximation arbitrarily close to the original distribution. Moreover, the queueing results obtained via these approaches are only numerical. Inspired by ....

....exp( GammaB Gamman ) exp( GammaaB Gamman t) 21) For large values of B, it may happen that is larger than 1 (due to the discretization error) In such a case, the value of M must be appropriately increased in order to ensure that is smaller than 1. Using the same terminology as [RoL97], we refer to G(t) as a pseudo Pareto distribution. Of course, the pseudo Pareto distribution can be made arbitrarily close to the exact Pareto distribution by letting B 1, N 1 and M Gamma1. As an illustration of the fitting method, a Pareto distribution with ccdf F (t) 1= 1 0:5 ....

S. Robert and J.-Y. Le Boudec "New Models for Pseudo Self-Similar Traffic," Performance Evaluation, Vol.30, pp.57-68, 1997.

....models and attempts to show how Dept. of Computing and Electrical Engineering, Heriot Watt University, Riccarton, Edinburgh EH14 4AS. Email: pjbk cee.hw.ac.uk, hal cee.hw.ac.uk self similar traffic will change the expected queue length. A self similar traffic model due to Robert and Le Boudec[5] is used to specify the input process to a queue. The matrix geometric techniques of Neuts[2, 3] are used to evaluate the steady state probabilities and calculate mean queue lengths. 2 Self Similarity For a time series, such as a set of interarrival times, self similarity is present if there are ....

....then X(t) is said to be self similar with Hurst parameter H. A Hurst parameter between 0 and 1 corresponds to fractional Brownian motion. Normal Brownian motion has H = 0:5. Measurements on Ethernet traffic have shown Hurst parameters ranging from 0.7 to 0. 99[1] Robert and Le Boudec[5] have developed a discrete time Markov chain which can represent self similar traffic. This model requires only three parameters and can describe a wide range of self similar behaviours. They assume that the input process can be in one of n states, in discrete time. When in state 1, a single ....

S. Robert and J.-Y. Le Boudec. New models for pseudo self-similar traffic. Performance Evaluation, 30(1):57--68, 1997.

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Robert, S. and Le Boudec, J. (1997). New models for pseudo self-similar traffic. Performance Evaluation, 30(1--2):57--68.

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S. Robert, J.Y. Le Boudec, "New Models for Pseudo Self-Similar Traffic," Performance Evaluation, Vol. 30, No. 1--2, pp. 57--68, Jul. 1997.

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S. Robert and J.Y. Le Boudec, New Models for Pseudo Self-Similar Traffic, Performance Evaluation, Vol.30, No.1-2, pp.57--68, 1997.

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