## The Impact of Self-Similarity on Network Performance Analysis (1995)

Citations: | 14 - 0 self |

### BibTeX

@TECHREPORT{Morin95theimpact,

author = {Patrick R. Morin},

title = {The Impact of Self-Similarity on Network Performance Analysis},

institution = {},

year = {1995}

}

### OpenURL

### Abstract

Recently, statistical analysis of high-resolution measurements of several types of network traffic has shown that many type of network traffic are self-similar or fractal in nature. This report gives an overview of self-similarity and examines the effect of self-similar inputs on the performance of asynchronous transfer mode (ATM) switches. This is done through the use of trace based simulation using actual Ethernet traffic traces. The results of these simulations suggest that self-similarity has an adverse effect on the performance of ATM switches and that certain suggested bandwidth allocation policies for ATM switches will significantly outperform others in the presence of self-similarity. ii Acknowledgements I would like to acknowledge several people who have helped with this project: Mike Devetsikiotis for providing me with numerous papers addressing the topic of selfsimilarity and for introducing me to several members of the Bellcore research team, Rob Tyson for providing me wi...

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Citation Context ... : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 15 viii Chapter 1 Introduction Recently, statistical analysis of Ethernet traffic measurements taken at Bellcore labs and described in =-=[LTWW94a]-=- has shown that Ethernet traffic is self-similar or fractal in nature. Other studies have shown that self-similarity is a feature Variable-BitRate Video Traffic [BSTW94]. Work done at Lawrence Berkele... |

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Citation Context ...own that Ethernet traffic is self-similar or fractal in nature. Other studies have shown that self-similarity is a feature Variable-BitRate Video Traffic [BSTW94]. Work done at Lawrence Berkeley Labs =-=[PF94]-=- shows that certain major components of internet traffic exhibit self-similarity. Studies of Common Channel Signaling Networks (CCSNs) [DMRW94], and Integrated Services Digital Networks (IDSN) [GW94] ... |

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Citation Context ... [PF94] shows that certain major components of internet traffic exhibit self-similarity. Studies of Common Channel Signaling Networks (CCSNs) [DMRW94], and Integrated Services Digital Networks (IDSN) =-=[GW94]-=- have also uncovered self-similarity. 1.1 An Intuitive Description of Self-Similarity Intuitively, self-similar phenomena display structural similarities across a wide range of time scales. This intui... |

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Citation Context ...a fast method of generating synthetic traffic traces for use in simulations. Currently. there are a number of popular approaches to generating self-similar sample paths. One such method, described in =-=[LTWW94b]-=- consists of aggregating a number of renewal rewards processes to obtain a self-similar process. This approach has the problem that one must trade off speed for the degree of self-similarity, as incre... |

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Citation Context ...at the communication bursts produced by individual users have a heavy-tailed distribution. This conclusion is supported by in depth analysis of Ethernet [LTWW94a] and wide area network traffic traces =-=[P95]-=-. Chapter 4. Dealing With Self-Similarity 21 4.2 Generating Synthetic Traffic Traces While an Ethernet monitor such as the one built at Bellcore labs is useful for gathering trace data, not everyone h... |

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Citation Context ...y, but unlike the previous approach, this method is not easily parallelized. A third method of generating a self-similar sample path is the "Random Midpoint Displacement" (RMD) Algorithm des=-=cribed in [LEWW95]-=-. This method has the property that it is fast and has reportedly been used to generate 260,000 observations in less than 2 minutes on a SPARCstation 20. The method does have the problem that the actu... |

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Citation Context ... the circuit that is built will meet the application's requirements. The choice of metrics used to define quality of service is still an open question. Some of the most commonly suggested metrics are =-=[BCDB95]-=-: Cell Loss Rate: defined as the number of cells which do not arrive at their destination (due to buffer overflow in switches) divided by the total number of cells Chapter 2. Networking 8 sent. Latenc... |

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Citation Context ...m) )sbm \Gamma1 ; as m !1 (3.13) where b is a finite positive constant independent of m. This has serious implications for classical statistical tests and the calculation of confidence intervals (see =-=[B86]-=- and [HRRS86]) since the usual measures of standard deviation are wrong by a factor that tends to infinity as the sample size increases. Chapter 4 Dealing With Self-Similarity By now the attentive rea... |

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Citation Context ...e Ethernet communications network. Readers not familiar with Ethernet may find the following description useful. Network experts may safely skip this section. The following discussion closely follows =-=[SH80]-=-. Ethernet is a broadcast multiaccess system for local area networking with distributed control. In an Ethernet network, a number of stations are connected to a single channel. When a station wants to... |

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Citation Context ... 2. Networking 7 output buffering. Because ATM switches operate at very high speeds, the cost of large buffers tends to be prohibitive. Typical buffer sizes are 256, 1000, 2000, 5000, and 11000 cells =-=[R93]-=-. - - - - - - - - - - Switch Fabric Input Ports Output Ports Figure 2.1: A simple model of an ATM switch An ATM network is composed of a number of switches interconnected with fiber optic links. ATM i... |

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Citation Context ... It should also be noted that although FGN is a Gaussian process, an FGN sample path can be transformed into a sample path with arbitrary marginal distribution while maintaining the Hurst parameter H =-=[HDLK95]-=-. 4.1.5 Fractional ARIMA(p,d,q) Processes The following definition is taken from [LTWW94a]. A fractional ARIMA(p,d,q) process is defined as a stochastic process X = (X k : k = 0; 1; 2; :::) represente... |

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Citation Context ...ellcore labs and described in [LTWW94a] has shown that Ethernet traffic is self-similar or fractal in nature. Other studies have shown that self-similarity is a feature Variable-BitRate Video Traffic =-=[BSTW94]-=-. Work done at Lawrence Berkeley Labs [PF94] shows that certain major components of internet traffic exhibit self-similarity. Studies of Common Channel Signaling Networks (CCSNs) [DMRW94], and Integra... |

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Citation Context ... H obtained using the two methods. 4.1.3 Stochastic Modeling of Self-Similar Phenomenon Self-similarity is not a new phenomenon, and has been studied extensively in several fields including hydrology =-=[MH78]-=- and economics [M69]. Because of this, several formal mathematical models have already been developed which exhibit self-similarity. However, because of the abstract nature of these models, it is ofte... |

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Citation Context ... skip this section. The following description of ATM is by no means complete. For a more thorough description of cell networking in general and ATM in particular, the interested reader is referred to =-=[P93]-=-. Data in an ATM network is transported via small fixed length packets called cells. Each cell is 53 bytes long and is broken into 48 bytes of data and 5 bytes of header. An ATM switch is composed of ... |