一种新的三环网络TL(N;1,s,s+1)直径求解方法

A new method to calculate the diameter of triple-loop networks TL(N;1,s,s+1)

基于多环网络的直径是衡量网络效率的重要指标,提出了一种新的有向三环网络TL(N;1,s,s+1)的直径求解方法——等价三叉树方法,并得到了一种新的直观图——三叉树.采用C#语言和SQL Server2000仿真实现了三叉树的结构模型.研究了该三叉树的性质,给出了三叉树的构造算法.找到了该族三环网络直径d(N;1,s,s+1)最大值、最小值的分布规律.仿真结果表明:直径的最大值随N值的增加呈有规律的锯齿状波动增加,直径的最小值随N值的增加呈有规律的阶梯状增加,并给出了直径d(N;1,s,s+1)的上界与下界的显式公式.

The diameter of multi-loop networks is an important indicator to measure network ef- ficiency, a new method, equivalent ternarytree method, to calculate the diameter of directed triple-loop networks TL （N ; 1, s, s ＋ 1） is presented. A new diagram, ternarytree, is obtained by this method. The structural model of ternarytree is stimulated which makes use of C-Sharp and SQL Server2000. The attributes of ternarytree are studied and the algorithm of construc- ting ternarytree is presented. The distribution rule of the maximum diameter values and the minimum diameter values of this triple-loop networks family are found. The simulating results show that the maximum diameter value is regular zigzag rising with the rising N value, the minimum diameter value is regular stair-stepping rising with the rising N value. The simple formula to express the diameter of upper bound and lower bound, d （N ; 1, s, s＋1）, is presen- ted.