关于有向双环网络G(N;r,s)平均直径的研究

On the average diameter of directed double-loop networks G(N;r,s)

针对有向双环网络的最小路径图,给出了一个快速计算有向双环网络平均直径的高效算法.根据该算法,只要知道有向双环网络G(N;r,s)的3个参数N,r和s,就能计算出L-型瓦的4个参数a,b,p和q,从而计算出平均直径.对直径与平均直径之间的关系进行了仿真研究,结果表明:在一个无限族中,直径与平均直径的分布呈轴对称图形;同一网络的平均直径约等于直径的一半;在任意无限族中,当直径达到下界值时,平均直径不一定达到下界值,但当平均直径达到下界值时,直径一定达到下界值.最终表明平均直径比直径能更好地衡量网络传输效率.

A rapid algorithm to compute its average diameter is provided from the shortest path diagram of directed double-loop network. According to this algorithm, four parameters a,b,p and q of L-shaped tile can be worked out if three parameters N,r and s of G（N;r,s） are known, and thus the average diameter of directed double-loop network can be obtained by calculating afterwards. Through the simulation study of the relationship between the diameter and average diameter, the results show that the distribution of the diameter and average diameter are all axis-symmetrical figure in one infinite family and average diameter approaches to a half of the diameter to one network. For anyone of infinite families, average diameter doesn＇t always obtain minimum value even though diameter obtains minimum value, but if average diameter obtains minimum value, the diameter must obtain minimum value. The experiments show that average diameter is the better parameter to measure transmission efficiency about networks than diameter.