## New Models for Pseudo Self-Similar Traffic (1996)

Venue: | Performance Evaluation |

Citations: | 23 - 1 self |

### BibTeX

@ARTICLE{Robert96newmodels,

author = {Stephan Robert and Jean-yves Le Boudec},

title = {New Models for Pseudo Self-Similar Traffic},

journal = {Performance Evaluation},

year = {1996},

volume = {30},

pages = {57--68}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 self-similarity 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 re-use the well-known analytical queuing theory techniques developed in the past in order to evaluate network performance. The t...

### Citations

1765 | On The Self-Similar Nature of Ethernet Traffic
- Leland, Taqqu, et al.
- 1994
(Show Context)
Citation Context ...ses of finite order, all finite Markov chains (including semi-Markov processes) are included in the first category. In the second category, we have the fractional Brownian motion [5], arima processes =-=[6]and chaoti-=-c maps [7] which have long-range dependences. However, if we look at this definition, we see that a process having "long term dependences", but which is limited is considered as a short term... |

137 |
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- 2004
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Citation Context ... rough random fractal curves, to 1 corresponding to rather smooth looking random fractals. In fact, there exists a direct relation between H and the fractal dimension of the graph of a random fractal =-=[3]-=-. Ordinary Brownian motion is a process X(t) with Gaussian increments and var(X(t 2 ) \Gamma X(t 1 )) / jt 2 \Gamma t 1 j 2H where H = 1=2. The generalization of parameters 0 ! H ! 1 is called fractio... |

105 |
E¢ cient and portable combined random number generators
- L’Ecuyer
- 1988
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Citation Context ...efore, we used an iterative method. Suppose for example that a = 10 and that the Markov chain is in the first state, then a number between 0 and 1 is generated with a reliable random number generator =-=[13]-=-. If the next number is less than 1=a = 1=10, the next state is not 2 but between 3 and n. The procedure continues until the random number is more than 1=a or until the last state is reached. To resum... |

103 |
Aggregation of variables in dynamic systems
- Simon, Ando
- 1961
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Citation Context ...served in other domains than computing: in economics, in biology, genetics, social sciences. The pioneers in this domain are Simon and Ando who studied several study-cases in economics and in physics =-=[11]-=-. What they stated is that aggregation of variables in a nearly decomposable system must separate the analysis of the short term and long term dynamics. They proved two major theorems. The first says ... |

99 | High time resolution measurements and analysis of LAN traffic
- Leland, Wilson
- 1991
(Show Context)
Citation Context ... same for 10 s, 100 s, 1000 s, 10000 s and is distinctively different from a pure noise. However in the order of days, researchers at Bellcore have observed a stabilization of the index of dispersion =-=[8]-=- indicating a lack of self-similarity. So, according to the definition, a short term dependences process would be sufficient to model lan traffic. The difference with other processes (Poisson, on-off,... |

68 |
A measurement study of diskless workstation tra c on an ethernet
- Gusella
- 1990
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Citation Context ... 0:5, which is very appearent for the 3 and 5 state processes in Figures 2, 3 and 4. 4 Fitting Based on measurements, a lot of fitting procedures have been proposed in the literature (see for example =-=[16]-=-, [17]). Ours is based on the Markov chain described in (section 2.2). Here, we fit only two parameters: mean and Hurst parameter (plus the number of states in the Markov chain). As seen in (section 2... |

55 |
Robust R,/S analysis of long-run serial correlation
- Mandelbrot, Taqqu
- 1979
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Citation Context ...0 (var(X (m) )=oe 2 ) against log 10 (m). The estimated slope fi gives an estimate of H : H = 1 \Gamma fi=2. Note that other methods are available to estimate H: R/S statistics proposed by Mandelbrot =-=[15]-=- and periodograms [6]. In our context, we estimate the local Hurst parameter H l . In Figures 2, 3 and 4, the variance-time plot is given for a Markov chain having the structure described in 2.3. In a... |

42 |
Long-Range Dependence: A Review," in Statistics: An Appraisal
- Cox
- 1984
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Citation Context ...ly undistinguable. Then, if X(t) is accelerated by a factor r: X(rt), it is rescaled by dividing the amplitudes by r H . 2 New model 2.1 Considerations on pseudo long-range dependences Mathematically =-=[4]-=-, the difference between short-range and long-range dependencies is clear: for a shortrange dependent process. ffl P 1 =0 cov(X t ; X t+ ) is convergent ffl spectrum at 0 is finite ffl var(X (m) ) is ... |

32 | Chaotic maps as models of packet traffic - Erramilli, Singh, et al. - 1994 |

25 | Studies on a model for connectionless traffic, based on fractional Brownian motion
- Norros
- 1993
(Show Context)
Citation Context ...moving average processes of finite order, all finite Markov chains (including semi-Markov processes) are included in the first category. In the second category, we have the fractional Brownian motion =-=[5], arima pr-=-ocesses [6]and chaotic maps [7] which have long-range dependences. However, if we look at this definition, we see that a process having "long term dependences", but which is limited is consi... |

17 |
Long-term storage of reservoirs: an experimental study. Transactions of the the american society of civil engineers
- Hurst
- 1951
(Show Context)
Citation Context ...ality traffic measurements have revealed that traffic behaves quite differently to what has been assumed until now. It has been observed that a large number of traffic sources produces a self-similar =-=[1, 2]-=- behavior over large time scales. Imagine a cluster composed of smaller clusters which look almost identical to the entire cluster, but scaled down by some factor. Each of these smaller clusters is ag... |

9 |
Can Self-Similar Traffic be modeled by Markovian processes
- Robert, LeBoudec
- 1996
(Show Context)
Citation Context ...ource is the absence of a natural length of burst in the first case as in the second. At each timescale, we observe bursty periods separated by less bursty subperiods like in the measured LAN traffic =-=[14, 6]-=-. In contrast, the classical sources behave very differently because the correlation is present in general only at one timescale. Even through the traffic could be very 8 0 10 0 1 10 0 2 10 0 3 10 0 4... |

3 |
Fractional Brownian Motions, Frational Noises and Applications
- Mandelbrot
- 1968
(Show Context)
Citation Context ...ality traffic measurements have revealed that traffic behaves quite differently to what has been assumed until now. It has been observed that a large number of traffic sources produces a self-similar =-=[1, 2]-=- behavior over large time scales. Imagine a cluster composed of smaller clusters which look almost identical to the entire cluster, but scaled down by some factor. Each of these smaller clusters is ag... |

2 |
Wich Arrival Law Parameters Are Decisive for Queuing System Performance
- Grunenfelder, Robert
(Show Context)
Citation Context ...which is very appearent for the 3 and 5 state processes in Figures 2, 3 and 4. 4 Fitting Based on measurements, a lot of fitting procedures have been proposed in the literature (see for example [16], =-=[17]-=-). Ours is based on the Markov chain described in (section 2.2). Here, we fit only two parameters: mean and Hurst parameter (plus the number of states in the Markov chain). As seen in (section 2.4), E... |