网络流量的多分形广义柯西模型理论

This proposal intends to explore new model of teletraffic, which may truly fit in with real data of multi-fractal traffic. We shall establish the theory of multi-fractal generalized Cauchy (GC) traffic model, which consists of the main tasks as follows. First, which is the kernel of the project, is to establish the autocorrelation function of the multi-fractal GC process. With it, local self-similarity of traffic may be characterized by fractal dimension function D(t) on the one hand. On the other hand, global behavior of traffic, such as long-range dependence, may be described by the Hurst exponent function H(t). Both are on the point by point basis. In addition, commonly used fractal models of traffic, such as fractional Gaussian noise, will all be special cases of the proposed new model of traffic. The second task is to establish simulation method of multi-fractal GC process. The third is to establish the power spectrum of multi-fractal generalized GC process, revealing novel multi-fractal behavior of traffic in frequency domain.

此申请项目探索更符合实际网络流量的新模型. 项目欲建立流量的多分形广义柯西模型理论. 该理论含以下主要研究任务. (1)建立多分形广义柯西过程的自相关函数. 以能用时变分形维数D(t)与时变Hurst指数H(t)，按时刻分别刻画流量的瞬时自相似性(局部特性)与瞬时长相关性(全局特性). 常用的分形流量模型（如分数阶高斯过程等）都将成为此模型的特殊情形. (2) 建立多分形广义柯西过程的仿真方法. (3) 建立多分形广义柯西过程的功率谱, 以能在频域中揭示流量新多分形特性.

此项目的题目是“网络流量的多分形广义柯西模型理论”. 项目创建了多分形广义柯西过程模型理论，并把该模型用来解释网络流量的多分形特性. 此外，项目还做了其它若干相关有创新性和进展性的工作（如创建分形流量延迟界的初步理论架构、创建了网络流量测量记录长度的参考准则，等）. 报告正文将简要说明20项成果. 本项目共发表论著46份，其中SCI检索论文26篇（含1篇ESI高被引论文），国外出版专著1本. 项目负责人于2020年入选1996-2017的22年和1996-2018的23年世界前10万科学家榜单，于2016-2020年入选2015年、2016年、2017年、2018年、2019年中国高被引学者榜单.