有向双环网络的三紧优性研究及随机步长仿真

发布时间：2018-10-12 12:26

【摘要】：对于需要超高速的通信网络的场合,如超级计算机CPU集群之间的通信网络,网络的信息通信延迟无疑是最重要的。单个CPU的运算速度无疑是极快速的,但是倘若它们之间的通信网络的信息通信延迟较大,整体的运算速度就会大打折扣。因此,研究信息通信延迟低的网络就非常重要。有向双环网络就是运用在这些场合的一种通信网络。论文研究了有向双环网络的信息通信延迟,提出了“直径方差”和“三紧优性”的概念,通过数学方法的理论推导,以及编程仿真,证明了“三紧优”的有向双环网络就是信息通信延迟最小的网络,并在仿真实例中找出了“三紧优”的一簇有向双环网络。论文还对随机步长的网络的“三紧优性”进行了研究,通过编程仿真,验证了随机步长的有向双环网络优于固定步长的有向双环网络的观点,并在仿真实例中找出了“三紧优”的一簇随机步长有向双环网络。论文的主要工作有:1)从数学的理论推导上,提出了“分步路径法”,证明了“顶点关系树”的各项性质,推导出有向双环网络直径的上界和下界,推导出有向双环网络平均直径的显式公式,推导出平均直径的上界和下界。发现了网络通信中的“木桶效应”,提出了直径方差的定义公式,推导出直径方差的显式公式和一个近似估计公式。得出了线性变化的统计数组的样本方差的近似估计公式。推导出直径方差的上界和下界。给出了有向双环网络“三紧优”的定义。2)从编程仿真上,提出了有向双环网络直径、平均直径、直径方差的求解算法,并仿真,在仿真实例中找出了“三紧优”的有向双环网络。提出了随机步长有向双环网络的生成算法,并仿真。提出随机步长有向双环网络直径、平均直径、直径方差的求解算法,给出伪代码并仿真,在仿真实例中找出了“三紧优”的随机步长有向双环网络。
[Abstract]:The information communication delay of the network is undoubtedly the most important in the case of super high speed communication network, such as the communication network between the CPU clusters of supercomputers. The operation speed of a single CPU is undoubtedly very fast, but if the communication network between them has a large information communication delay, the overall computing speed will be greatly reduced. Therefore, it is very important to study the network with low information and communication delay. A directional double loop network is a communication network used in these situations. In this paper, the information communication delay of directional double loop network is studied, and the concepts of "diameter variance" and "three compactness optimality" are proposed. It is proved that the "triple compact optimal" directed double loop network is the one with the smallest information communication delay. A cluster of directional double loop networks with "three compact optimal" is found in the simulation example. The paper also studies the "three compactness optimality" of the random step size network. Through programming and simulation, the viewpoint that the random step size directional double loop network is superior to the fixed step size directional double loop network is verified. A cluster of random step size directed double loop networks with "three compactness optimization" is found in the simulation example. The main work of this paper is as follows: 1) based on the theoretical derivation of mathematics, a step path method is proposed to prove the properties of the vertex relation tree, and the upper and lower bounds of the diameters of the directed double-ring network are derived. An explicit formula for the mean diameter of a directional double loop network is derived, and the upper and lower bounds of the mean diameter are derived. The "barrel effect" in network communication is found, the definition formula of diameter variance is proposed, the explicit formula of diameter variance and an approximate estimation formula are derived. The approximate estimation formula of sample variance of a linearly varying statistical array is obtained. The upper and lower bounds of diameter variance are derived. In this paper, the definition of "three compactness optimization" of directional double-ring network is given. 2) from the point of view of programming simulation, an algorithm for solving diameters, mean diameters and diameters variance of directed double-ring networks is proposed and simulated. In the simulation example, the "three compact optimal" directional double loop network is found. A random step size directed double loop network generation algorithm is proposed and simulated. This paper presents an algorithm for solving the diameter, mean diameter and variance of random step size directional double loop network. The pseudo code is given and simulated. In the simulation example, the random step size directional double loop network with three compactness optimization is found out.
【学位授予单位】：安徽工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP393.02

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