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20
The chaotic nature of TCP congestion control
, 2000
"... Abstract In this paper we demonstrate how TCP congestion control can show chaotic behavior. We demonstrate the major features of chaotic systems in TCPlIP networks with examples. These features include unpredictability, extreme sensitivity to initial conditions and odd periodicity. Previous work h ..."
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Cited by 118 (4 self)
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Abstract In this paper we demonstrate how TCP congestion control can show chaotic behavior. We demonstrate the major features of chaotic systems in TCPlIP networks with examples. These features include unpredictability, extreme sensitivity to initial conditions and odd periodicity. Previous work has shown the fractal nature of aggregate TCPAP traffic and one explanation to this phenomenon was that traffic can be approximated by a large number of ON/OFF sources where the random ON and/or OFF periods are of length described by a heavy tailed distribution. In this paper we show that this argument is not necessary to explain selfsimilarity, neither randomness is required. Rather, TCP itself as a deterministic process creates chaos, which generates selfsimilarity. This property is inherent in todays TCPlIP networks and it is independent of higher layer applications or protocols. The two causes: heavy tailed ONlOFF and chaotic TCP together contribute to the phenomena, called fractal nature of Internet traffic. KeywordsTCP congestion control, fractal traffic, chaotic models. I.
Fractal traffic: measurements, modelling and performance evaluation
 in Proc. IEEE INFOCOM '95
, 1995
"... Observations of both Ethernet traffic and variable bit rate (VBR) video traffic have demonstrated that these traffics exhibit “selfsimilarity ” and/or infinit l e asymptotic index of dispersion for counts (IDC). We report here on measurements of traffic an a commercialpublic broadband network where ..."
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Cited by 45 (7 self)
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Observations of both Ethernet traffic and variable bit rate (VBR) video traffic have demonstrated that these traffics exhibit “selfsimilarity ” and/or infinit l e asymptotic index of dispersion for counts (IDC). We report here on measurements of traffic an a commercialpublic broadband network where similar characteristics have been observed. For the purpose of analysis and dimensioning of the central links of an ATM network we analyse in this paper the performance of a single server queue fed by Gaussian trafic with infjlnite IDC. The analysis leads to an approximation fo,r the performance of a queue in which the arriving trafic is “fractal ” Gaussian and consequently where there does not exist a dominant negativeexponential tail. The term ufractal ” is used here in the sense thtzt the autocovariance of the traffic exhibits selfsimilarity, that is to say, where the autocovariance of an aggregate of the trafic is the same, or asymptotically the same for large time lags, as the original traffic. We are not concerned with proving or exploiting this selfsimilarity property as such, but only with performancle analysis techniques which are effective for such processes. In order to be able to test the performance analysis formulae, we show that trafic with the same arutocovariawe as measured an a real network over a wide range of lags (sufficiently wide a range for the traffic to be equivalent from the point of view of queueing performance) can be generated as a mixture of two Gaussian AR(1) processes. In this way we demonstrate that the analytic performance formulae are accurate. 1
Fluid Queues with Longtailed Activity Period Distributions
, 1997
"... This is a survey paper on fluid queues, with a strong emphasis on recent attempts to represent phenomena like longrange dependence. The central model of the paper is a fluid queueing system fed by N independent sources that alternate between silence and activity periods. The distribution of the a ..."
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Cited by 31 (1 self)
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This is a survey paper on fluid queues, with a strong emphasis on recent attempts to represent phenomena like longrange dependence. The central model of the paper is a fluid queueing system fed by N independent sources that alternate between silence and activity periods. The distribution of the activity periods of at least one source is assumed to be longtailed, which may give rise to longrange dependence. We consider the effect of this tail behaviour on the steadystate distributions of the buffer content at embedded points in time and at arbitrary time, and on the busy period distribution. Both exact results and bounds are discussed.
New Models for Pseudo SelfSimilar Traffic
 Performance Evaluation
, 1996
"... After measurements on a lan at Bellcore, it is known that data traffic is extremely variable on time scales ranging from milliseconds to days. The traffic behaves quite differently to what has been assumed until now; traffic sources were generally characterized by short term dependences but characte ..."
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Cited by 23 (1 self)
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After measurements on a lan at Bellcore, it is known that data traffic is extremely variable on time scales ranging from milliseconds to days. The traffic behaves quite differently to what has been assumed until now; traffic sources were generally characterized by short term dependences but characteristics of the measured traffic have shown that it is long term dependent. Therefore, new models (such as Fractional Brownian motion, arima processes and Chaotic maps) have been applied. Although they are not easily tractable, one big advantage of these models is that they give a good description of the traffic using few parameters. In this paper, we describe a Markov chain emulating selfsimilarity which is quite easy to manipulate and depends only on two parameters (plus the number of states in the Markov chain). 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. The t...
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 21 (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.
Regular Variation in a MultiSource Fluid Queue
 in ITC 15
, 1996
"... This paper considers a fluid queueing system, fed by N independent sources that alternate between silence and activity periods. We assume that the distribution of the activity periods of source 1 is a regularly varying function of index i , whereas all other sources have activity period distributi ..."
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Cited by 14 (5 self)
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This paper considers a fluid queueing system, fed by N independent sources that alternate between silence and activity periods. We assume that the distribution of the activity periods of source 1 is a regularly varying function of index i , whereas all other sources have activity period distributions with an exponential tail. In addition, we assume that the inflow rate of each of the sources, when active, exceeds the outflow rate of the buffer. Under these assumptions, we show that the tail of the buffer content distribution is regularly varying of index i +1. In the special case that i 2 (\Gamma2; \Gamma1), which implies longrange dependence of the input process, the buffer content does not even have a finite first moment. Based on the obtained results and on a conjecture for the case that the outflow rate of the buffer is not necessarily exceeded by the inflow rates of the sources, we suggest a simple, effectivebandwidthlike, connection admission rule. AMS Subject Classi...
The Autocorrelation of Double Intermittency Maps and the Simulation of Computer Packet Traffic
, 2003
"... Since the discovery in the early 1990's that packet traffic exhibits longrangedependence there has been considerable interest in finding system that could generate reliable pseudotraffic traces. One such system is a onedimensional chaotic map. We examine a particular instance of such maps. It is ..."
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Cited by 8 (2 self)
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Since the discovery in the early 1990's that packet traffic exhibits longrangedependence there has been considerable interest in finding system that could generate reliable pseudotraffic traces. One such system is a onedimensional chaotic map. We examine a particular instance of such maps. It is nonsmooth, but its nature is such that analytical results are easier to obtain. In particular we derive a theorem about the asymptotics of the autocorrelation. In the subsequent discussion, it is argued that to get a relevant description of packet traffic, one needs to venture beyond first and secondorder statistics.
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 2 (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).
Traffic Characterization for Heterogeneous Applications
 in Technical Report
, 2001
"... This report is a brief survey of schemes used for characterization of application traffic. We discuss the different kinds of applications, and their QoS requirements. Measurementbased, Statistical modelbased and Deterministic modelbased schemes are used to characterize traffic, and we elucidate e ..."
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Cited by 2 (0 self)
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This report is a brief survey of schemes used for characterization of application traffic. We discuss the different kinds of applications, and their QoS requirements. Measurementbased, Statistical modelbased and Deterministic modelbased schemes are used to characterize traffic, and we elucidate each scheme with an application. We look at selfsimilarity and, consequences of changes in network resources and flowcontrol algorithms on selfsimilar traffic. Finally, we cover a few parsimonious models for this kind of traffic.