<p>As the scale of P2P (Peer-to-Peer) networks continues to expand, the problems existing in the network will become increasingly apparent. There are a large number of users in the network who only download resources without uploading (known as free-riding behavior), which severely impacts the network operation. This paper combines P2P networks with queuing theory, using the arrival and service processes in queuing theory to analogize the dynamic changes of peers in the network, introducing differentiated services, synchronized multiple vacations, service peer repairable fault strategies, and establishing the Geo/Geo/<i>c</i>+<i>d</i> queuing model. The paper uses matrix-geometric and Gauss-Seidel iteration methods to obtain a series of performance measures for the system, analyzes the impact of parameter variations on performance measures using Matlab software, and also analyzes the expected benefits of two types of requesting peers and system benefit functions. Based on the set parameters, the optimal parameters that maximize system benefits are obtained. This approach aims to minimize the waiting time and losses of non free-riding peers, maximize system benefits, and encourage peers to share resources.</p>