On use of the alpha stable self-similar stochastic process to model aggregated VBR video traffic

1 .INTRODUCTIONThe conventional short range dependence (SRD) basedtraffic models such as Poisson or Markov, have beenproved not suitable for the analysis of network trafficwith long range dependence (LRD) . While use thesemodels on networktraffic withself-si milarity,LRD,theperformances of network,suchas buffer overflowprob-ability,cell lose probability,delay,etc.,would becomehigh and unstable. However ,recent researches tell us,self-si milarity and LRDare the most i mportant charac-…     

自相似模型仿真ATM网络VBR视频源研究

仿真过程采用了一种新的异步传输模式（ATM）视频源建模方法，即长期相关性分析和自相似模型方法，使用了自相似模型中的分形高斯噪声（FGN）模型。FGN过程的产生采用了Hosking算法和反变换法。在仿真具体实现过程中改进了现有FGN模型仿真算法的不足，从而使产生的过程既充分考虑到实际可变比特率（VBR）视频源序列的长期相关性，又兼顾了序列的短期相关性，同时给出了仿真结果与实际源统计特性的比较和验证。比较结果表明，自相似模型是一种理想的VBR视频源模型。     

一个基于多重随机二分法的流量仿真模型的算法设计

随着互联网流量的急剧增加,网络流量的特征也发生了很大变化,相应的需要网络流量模型也随之发展。在对实际城域网流量拟合的基础上,设计了一个基于Gamma分布和多重随机二分法的流量仿真模型。对仿真流量的评估证实,该模型不仅较好地刻画了网络流量的自相似特征,而且能够方便地控制仿真流量的自相似程度,从而为网络设计和网络设备测试中仿真流量负载的生成提供了一种新的算法。     

Self-similar measures on the Julia sets of polynomials

If the immediate basin of infinity of a polynomial P(z) contains at least one of its critical points, then there is a self-similar measure on its Julia set, and if all the critical points of P(z) lie in the immediate basin of in finity, then the self-similar measure is unique.     

Fractals generated by statistical contraction operators

In the theory of random fractal, there are two important classes of random sets, one is the class of fractals generated by the paths of stochastic processes and another one is the class of factals generated by statistical contraction operators. Now we will introduce some things about the probability basis and fractal properties of fractals in the last class. The probability basis contains (1) the convergence and measurability of a random recursive set K(ω) as a random element, (2) martingals property. The fractal properties include (3) the character of various similarity, (4) the separability property, (5) the support and zero-one law of distribution Pk=PK-1, (6) the Hausdorff dimension and Hausdorff exact measure function.     

Some fractal properties of a class of self-similar Markov processes

LetX=(Ω,F,F _t ,X _t , θ _t ,P ^x be a self-similar Markov process on (0, ∞). The exact Hausdorff measure function of the level sets are obtained. An appropriate condition is given under which the self-similar Markov process corresponds to a stable process, and some more fractal properties of the sample path ofX are obtained in this case. Supported by the National Natural Science Foundation of China Huang Lihu: born in March 1972, Ph. D graduate student     

Traffic Prediction in 3G Mobile Networks Based on Multifractal Exploration

Traffic prediction plays an integral role in telecommunication network planning and network optimization. In this paper, we investigate the traffic forecasting for data services in 3G mobile networks. Although the Box-Jenkins model has been proven to be appropriate for voice traffic (since the arrival of calls follows a Poisson distribution), it has been demonstrated that the Internet traffic exhibits statistical self-similarity and has to be modeled using the Fractional AutoRegressive Integrated Moving Average (FARIMA) process. However, a few studies have concluded that the FARIMA process may fail in modeling the Internet traffic. To this end, we conducted experiments on the modeling of benchmark Internet traffic and found that the FARIMA process fails because of the significant multifractal characteristic inherent in the traffic series. Thereafter, we investigate the traffic series of data services in a 3G mobile network from a province in China. Rich multifractal spectra are found in this series. Based on this observation, an integrated method combining the AutoRegressive Moving Average (ARMA) and FARIMA processes is applied. The obtained experimental results verify the effectiveness of the integrated prediction method.     

不动点为正m面体顶点的一类压缩函数满足开集条件的研究

设{Sj}nmj+1是R3上由Sj(a)=aj+λ(a-aj),j=1,2,…,nm定义的压缩函数系,其中nm表示正m面体的顶点数,aj∈R3表示正m面体的顶点,0<λ<1.给出了一个关于λ的条件,使得压缩函数{Sj}nmj+1当λ∈(0,pm]时满足开集条件,当λ=pm时满足相触条件.同时,给出了当0<λ≤pm时,压缩函数{Sj}nmj+1的吸引子Km的Hausdorff维数.     

两级自相似分形微流控浓度梯度芯片设计及性能分析

浓度梯度被广泛应用于趋化分析、细胞生长、DNA检测和毒性评价等诸多领域。传统浓度梯度生成方法具有效率低、梯度不精确、稳定性差等不足。本文基于经典圣诞树模型,设计了一种反应速度快、精度高,可生成稳定浓度梯度的两级自相似分形微流控浓度梯度芯片,并进行了仿真与实验研究。建立了多物理场耦合模型,在不同进样条件下,使用COMSOL Multiphysics进行了数值模拟。通过对归一化进样流量矩阵与浓度矩阵的耦合设置,得到丰富种类的浓度梯度分布。以去离子水和红色染料为样本进行实验验证,结果与仿真模拟具有较好的一致性,证明了两级自相似分形微流控浓度梯度芯片设计的合理性,其优势在于,无需重新设计微流道构型而只是简单调节进样流量比,便可以实现生成不同浓度梯度的实际需求。     

正交异性体中半无限长界面裂纹扩展问题的自相似解

基于复变函数方法，给出了两种正交异性体结合面间半无限长裂纹的自相似解，本文方法可以把复杂边界条件转化为简单的Keldysh-Sedov混合边值问题，迅速地得到问题的闭合解，并给出实例，通过对其叠加，可以得到任意复杂半无限裂纹问题的解析解，最后给出应力强度因子的图表。