Abstract: Based on analyzing the structure feature of WDM networks, this paper chooses some representative directed double-loop networks to study. It also provides the solutions of some congruence equations to compute the parameter values of L-shaped tile. According to the structure of L-shaped tile, it provides a formula to compute its network load. The experiment results demonstrate that there may be many load-balanced networks. For anyone of infinite families for [G(N;r,s)], the distribution of loads is axis symmetric figure, and there is a upper bound and a lower bound for loads. The network is called optimal load network when its load equals the lower bound. These results are important to design optimal double networks and improve transmission efficiency about networks.

Key words: Wavelength Division Multiplexing（WDM） networks, directed double-loop networks, network load, L-shaped tile, shortest path, infinite family

摘要： 针对WDM网络的结构特征，选择具有代表性的有向双环网络G（N；r，s）进行研究。给出一组同余方程，用于快速计算其L-型瓦图的四个参数。根据L-型瓦的结构，给出了计算有向双环网络的网络负荷公式。实验结果分析表明：有向双环网络的一个无限族中可能存在多个负荷平衡的网络。对于有向双环网络G（N；r，s）的任意一个无限族中，其网络负荷的分布呈轴对称图形。网络负荷存在上界和下界，负荷达到下界值的网络称为最优负荷网络。该研究成果对于设计最优双环网络和提高网络通信效率起到决定性的作用。

关键词: 波分复用（WDM）网络, 有向双环网络, 网络负荷, L-型瓦, 最短路径, 无限族