【摘要】：對(duì)于需要超高速的通信網(wǎng)絡(luò)的場(chǎng)合,如超級(jí)計(jì)算機(jī)CPU集群之間的通信網(wǎng)絡(luò),網(wǎng)絡(luò)的信息通信延遲無(wú)疑是最重要的。單個(gè)CPU的運(yùn)算速度無(wú)疑是極快速的,但是倘若它們之間的通信網(wǎng)絡(luò)的信息通信延遲較大,整體的運(yùn)算速度就會(huì)大打折扣。因此,研究信息通信延遲低的網(wǎng)絡(luò)就非常重要。有向雙環(huán)網(wǎng)絡(luò)就是運(yùn)用在這些場(chǎng)合的一種通信網(wǎng)絡(luò)。論文研究了有向雙環(huán)網(wǎng)絡(luò)的信息通信延遲,提出了“直徑方差”和“三緊優(yōu)性”的概念,通過(guò)數(shù)學(xué)方法的理論推導(dǎo),以及編程仿真,證明了“三緊優(yōu)”的有向雙環(huán)網(wǎng)絡(luò)就是信息通信延遲最小的網(wǎng)絡(luò),并在仿真實(shí)例中找出了“三緊優(yōu)”的一簇有向雙環(huán)網(wǎng)絡(luò)。論文還對(duì)隨機(jī)步長(zhǎng)的網(wǎng)絡(luò)的“三緊優(yōu)性”進(jìn)行了研究,通過(guò)編程仿真,驗(yàn)證了隨機(jī)步長(zhǎng)的有向雙環(huán)網(wǎng)絡(luò)優(yōu)于固定步長(zhǎng)的有向雙環(huán)網(wǎng)絡(luò)的觀點(diǎn),并在仿真實(shí)例中找出了“三緊優(yōu)”的一簇隨機(jī)步長(zhǎng)有向雙環(huán)網(wǎng)絡(luò)。論文的主要工作有:1)從數(shù)學(xué)的理論推導(dǎo)上,提出了“分步路徑法”,證明了“頂點(diǎn)關(guān)系樹(shù)”的各項(xiàng)性質(zhì),推導(dǎo)出有向雙環(huán)網(wǎng)絡(luò)直徑的上界和下界,推導(dǎo)出有向雙環(huán)網(wǎng)絡(luò)平均直徑的顯式公式,推導(dǎo)出平均直徑的上界和下界。發(fā)現(xiàn)了網(wǎng)絡(luò)通信中的“木桶效應(yīng)”,提出了直徑方差的定義公式,推導(dǎo)出直徑方差的顯式公式和一個(gè)近似估計(jì)公式。得出了線性變化的統(tǒng)計(jì)數(shù)組的樣本方差的近似估計(jì)公式。推導(dǎo)出直徑方差的上界和下界。給出了有向雙環(huán)網(wǎng)絡(luò)“三緊優(yōu)”的定義。2)從編程仿真上,提出了有向雙環(huán)網(wǎng)絡(luò)直徑、平均直徑、直徑方差的求解算法,并仿真,在仿真實(shí)例中找出了“三緊優(yōu)”的有向雙環(huán)網(wǎng)絡(luò)。提出了隨機(jī)步長(zhǎng)有向雙環(huán)網(wǎng)絡(luò)的生成算法,并仿真。提出隨機(jī)步長(zhǎng)有向雙環(huán)網(wǎng)絡(luò)直徑、平均直徑、直徑方差的求解算法,給出偽代碼并仿真,在仿真實(shí)例中找出了“三緊優(yōu)”的隨機(jī)步長(zhǎng)有向雙環(huán)網(wǎng)絡(luò)。
[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.
【學(xué)位授予單位】：安徽工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP393.02

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