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24
Practical TimeScale Fitting of SelfSimilar Traffic with MarkovModulated Poisson Process
, 2001
"... Recent measurements of packet/cell... In this paper, we first give some definitions of selfsimilarity. Then, we propose a fitting method for the selfsimilar traffic in terms of Markovmodulated Poisson process (MMPP). We construct an MMPP as the superposition of twostate MMPPs and fit it so as to ..."
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Cited by 22 (2 self)
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Recent measurements of packet/cell... In this paper, we first give some definitions of selfsimilarity. Then, we propose a fitting method for the selfsimilar traffic in terms of Markovmodulated Poisson process (MMPP). We construct an MMPP as the superposition of twostate MMPPs and fit it so as to match the variance function over several timescales. Numerical examples show that the variance function of the selfsimilar process can be well represented by that of resulting MMPPs. We also examine the queueing behavior of the resulting MMPP/D/1 queueing systems. We compare the analytical results of MMPP/D/1 with the simulation ones of the queueing system with selfsimilar input.
Traffic Source Modeling
, 1999
"... Designing and planning networks is often done by simulating the inuence of various traffic types. This simulation approach depends on reliable and realistic traffic models that are capable of covering first and secondorder statistics of the observed network traffic. In this report, an overview ove ..."
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Cited by 19 (5 self)
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Designing and planning networks is often done by simulating the inuence of various traffic types. This simulation approach depends on reliable and realistic traffic models that are capable of covering first and secondorder statistics of the observed network traffic. In this report, an overview over stateoftheart models for the simulation of network traffic will be given.
Markovian Modeling of Real Data Traffic: Heuristic phase type and MAP fitting of heavy tailed and fractal like samples
"... In order to support the effective use of telecommunication infrastructure, the "random" behavior of trac sources has been studied since the early days of telephony. Strange new features, like fractal like behavior and heavy tailed distributions were observed in high speed packet switched d ..."
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Cited by 18 (3 self)
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In order to support the effective use of telecommunication infrastructure, the "random" behavior of trac sources has been studied since the early days of telephony. Strange new features, like fractal like behavior and heavy tailed distributions were observed in high speed packet switched data networks in the early '90s. Since that time a fertile research aims to find proper models to describe these strange traffic features and to establish a robust method to design, dimension and operate such networks.
Multifractal Modeling of Counting Processes of LongRange Dependent Network Traffic
 Proceedings SCS Advanced Simulation Technologies Conference,San
, 1999
"... We study traffic streams through their counting process representation. We examine the longrangedependent (LRD) characteristics of such processes. We first show that the measured LRD traffic, as described by the interarrival time and packet size sequences, is sufficiently well approximated by a syn ..."
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Cited by 16 (8 self)
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We study traffic streams through their counting process representation. We examine the longrangedependent (LRD) characteristics of such processes. We first show that the measured LRD traffic, as described by the interarrival time and packet size sequences, is sufficiently well approximated by a synthesized stream formed by recording the counting state of the traffic at the start of each time slot. We then model these counting processes by constructing a multiplicative multifractal process. The model only contains two parameters. One is used to indicate the mean of the counting process; the other is employed to describe the variation of the traffic around the mean function. We show that this multifractal traffic characterization has well defined burstiness descriptors, and is easy to construct. We consider a single server queueing system which is loaded, on one hand, by the measured processes, and, on the other hand, by properly parameterized multifractal processes. In comparing the systemsize tail distributions, we demonstrate our model to effectively track the behavior exhibited by the system driven by the actual traffic processes.
Modeling and Analysis of PowerTail Distributions via Classical Teletraffic Methods
, 2000
"... e of exponentials The research was performed while this author was a Ph.D student at the Technion  Israel Institute of Technology This work was supported by the Israel Science Foundation administrated by the Academy of Science and Humanities 2 Starobinski and Sidi / Modeling and Analysis of ..."
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Cited by 14 (2 self)
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e of exponentials The research was performed while this author was a Ph.D student at the Technion  Israel Institute of Technology This work was supported by the Israel Science Foundation administrated by the Academy of Science and Humanities 2 Starobinski and Sidi / Modeling and Analysis of PowerTail Distributions 1. Introduction Recent studies have revealed that network trac exhibits burstiness over multiple time scales [15,22]. In many circumstances, powertail probability distributions have been found appropriate for capturing this salient feature (see [19] and references therein). A random variable X has a powertail distribution if its complementary cumulative distribution function (ccdf) F (t) satises F (t) = PrfX > tg ct as t !
A Markovian Point Process Exhibiting Multifractal Behavior And Its Application To Traffic Modeling
"... This paper introduces a set of Markovian Arrival Processes (MAPs) with a special structure exhibiting multifractal behavior. The considered MAP structure is motivated by the unnormalized Haar wavelet transform representation of finite sequences. A parameter fitting method is also proposed to approxi ..."
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Cited by 9 (2 self)
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This paper introduces a set of Markovian Arrival Processes (MAPs) with a special structure exhibiting multifractal behavior. The considered MAP structure is motivated by the unnormalized Haar wavelet transform representation of finite sequences. A parameter fitting method is also proposed to approximate the multifractal behavior of experimental data sets by MAPs of the given structure. The goodness of the fitting method is evaluated via the logmoment diagrams, the partition function, the Legendre transform, and also by comparing the queue length distribution resulting from the measured data set with the one resulted from the approximating MAP
Multifractal analysis and modeling of longrangedependent traffic
 in: Proc. of IEEE ICC
, 1999
"... ..."
On the Effects of the Packet Size Distribution on FEC Performance
"... For multimedia traffic like VBR video, knowledge of the average loss probability is not sufficient to determine the impact of loss on the perceived visual quality and on the possible ways of improving it, for example by forward error correction (FEC) and error concealment. In this paper we investiga ..."
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Cited by 4 (1 self)
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For multimedia traffic like VBR video, knowledge of the average loss probability is not sufficient to determine the impact of loss on the perceived visual quality and on the possible ways of improving it, for example by forward error correction (FEC) and error concealment. In this paper we investigate how the packet size distribution affects the packet loss process, i.e. the probability of consecutive losses and the distribution of the number of packets lost in a block of packets and the related FEC performance. We present an exact mathematical model for the loss process of an MMPP+MMPP/E r /1/K queue and compare the results of the model to simulations performed with various other packet size distributions (PSDs), among others, the measured PSD from an Internet backbone. The results show that analytical models of the PSD matching the first three moments (mean,variance and skewness) of the empirical PSD can be used to evaluate the performance of FEC in real networks. We conclude that the exponential PSD, though it is not a worst case scenario, is a good approximation for the PSD of today's Internet to evaluate FEC performance. We also conclude that the packet size distribution affects the packet loss process and thus the efficiency of FEC mainly in access networks where a single multimedia stream might affect the multiplexing behavior. We evaluate how the PSD affects the accuracy of the widely used Gilbert model to calculate FEC performance and conclude that the Gilbert model can capture loss correlations better if the CoV of the PSD is high.
Modeling and evaluation of pseudo selfsimilar traffic with infinitestate Petri nets
 Proc. of the Workshop on Formal Methods in Telecommunications
, 1999
"... We address the suitability of a recently suggested approach for approximating selfsimilar traffic with a Markovian model. The phasetype nature of the proposed approach is identified and used to transform it from the discretetime to the continuoustime domain. We then investigate the performance ..."
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Cited by 4 (1 self)
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We address the suitability of a recently suggested approach for approximating selfsimilar traffic with a Markovian model. The phasetype nature of the proposed approach is identified and used to transform it from the discretetime to the continuoustime domain. We then investigate the performance of a simple queueing system subject to selfsimilar arrival traffic, thereby comparing the results of tracedriven simulation with a measured selfsimilar trace to those derived from a numerical analysis of the suggested model. The numerical investigations are performed using a special class of stochastic Petri nets which is particularly suited for analyzing queueingmodel like situations. Our results indicate that the suggested Markovian traffic model needs still to be improved, even though the properties of selfsimilarity per se are well approximated.
On a Markov Modulated Chain Exhibiting SelfSimilarities Over Finite Timescale
, 1996
"... Recent papers have pointed out that data traffic exhibits selfsimilarity, but selfsimilarity is observed only on a finite timescale. In order to account for that, we introduce the concept of pseudo longrange dependences. In this paper, we describe a Modulated Markov process producing selfsimilar ..."
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Cited by 3 (0 self)
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Recent papers have pointed out that data traffic exhibits selfsimilarity, but selfsimilarity is observed only on a finite timescale. In order to account for that, we introduce the concept of pseudo longrange dependences. In this paper, we describe a Modulated Markov process producing selfsimilarity on a finite timescale; the process is quite easy to manipulate and depends only on three parameters (two real numbers and one integer). An advantage of using it is that it is possible to reuse the wellknown analytical queuing theory techniques developed in the past in order to evaluate network performance. A quantitative method based on the decomposability theory of Courtois is given to evaluate the domain of validity where the process exhibits pseudo longrange dependences. The validation on a queuing problem is also discussed. Finally, we analyze the inputs of a statistical multiplexer in the context of a project called Scalability Enhancements for ConnectionOriented Networks (SCONE).