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Multifractal and Gaussian fractional sum-difference models for Internet traffic

机译：互联网流量的多重分形和高斯分数和差模型

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A multifractal fractional sum-difference model (MFSD) is a monotone transformation of a Gaussian fractional sum-difference model (GFSD). The GFSD is the sum of two independent components: a moving sum of length two of discrete fractional Gaussian noise (fGn); and white noise. Internet traffic packet interarrival times are very well modeled by an MFSD in which the marginal distribution is Weibull; this is validated by extensive model checking for 715,665,213 measured arrival times on three Internet links. The simplicity of the model provides a mathematical tractability that results in a foundation for understanding the statistical properties of the arrival process. The current foundation is time scaling: properties of aggregate arrivals in successive equal-length time intervals and how the properties change with the interval length. This scaling is also the basis for the widely discussed multifractal wavelet models. The MFSD provides a more fundamehtal foundation that is based on how changes in the fGn and white noise components result in changes in the arrival process as various factors change such as the aggregation time length or the traffic packet rate. Logistic models relate the MFSD model parameters to the packet rate, so only the rate needs to be specified in using the MFSD model to generate synthetic packet arrivals for network engineering simulation studies. (C) 2016 Elsevier B.V. All rights reserved.
机译：多重分数分数和差模型（MFSD）是高斯分数和差模型（GFSD）的单调变换。 GFSD是两个独立分量的总和：离散分数高斯噪声（fGn）的长度2的移动总和；和白噪声。 MFSD很好地模拟了互联网流量数据包的到达时间，其中边际分布为Weibull。广泛的模型检查通过三个Internet链接上的715,665,213实测到达时间对此进行了验证。该模型的简单性提供了数学上的易处理性，从而为理解到达过程的统计属性奠定了基础。当前的基础是时间缩放：连续等长时间间隔内的集合到达属性以及该属性如何随间隔长度变化。这种缩放比例也是广泛讨论的多分形小波模型的基础。 MFSD提供了更为基础的基础，该基础基于fGn和白噪声分量的变化如何随着各种因素（例如聚合时间长度或流量包速率）的变化而导致到达过程的变化。 Logistic模型将MFSD模型参数与数据包速率相关联，因此在使用MFSD模型生成用于网络工程仿真研究的综合数据包到达时，仅需要指定速率。 （C）2016 Elsevier B.V.保留所有权利。

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