P2P（点对点）网络系统为文件的共享与传输提供了高效的平台。本项目拟研究存在线路故障的P2P网络系统。在满足终端下载需求的条件下，为了尽量减小网络堵塞，我们尝试引入“缺项addition-min模糊关系不等式”，通过优化建模和求解，得到最优的流量控制方案。在此基础上，我们又进一步探讨无故障系统的稳定性，寻求能够承受更多线路故障的最优流量控制方案。这两方面的研究都需要构建以缺项addition-min模糊关系不等式为约束条件的优化模型。基于特定的约束条件，我们将给出这些优化模型的求解算法，并验证算法可行性和计算复杂度，再通过P2P模拟器进行仿真模拟，验证所得最优解的有效性。本项目的预期成果将有效提高P2P网络系统的运行效率和稳定性。

P2P network system supplies efficient platform for file sharing and transmission. In this project we will investigate P2P network system with line fault. In order to decrease the network congestion, satisfying the download requirement of the terminals, we try to introduce the so-called absent-term addition-min fuzzy relation inequality. After optimization modeling and resolution, we are expected to obtain the optimal flow control scheme. Based on the previous research, we further discuss the stability in P2P network without line fault. The object is to find the optimal flow control scheme bearing more line faults. Study on both aspects mentioned above requires establishment of the optimization models subject to absent-term addition-min fuzzy relation inequality. Considering the specific constraints of these models, we will propose their resolution algorithms respectively. Feasibility and computational complexity will also be checked. Besides, P2P simulator will help us to check the validity of the obtained optimal solution by simulation experiment. The results obtained in this project are expected to improve the running effectiveness and stability significantly.