To improve the performance of Peer-to-Peer (P2P) networks and reduce energy consumption while minimizing “free-riding” behavior, a queuing model is utilized to abstract dynamic changes of peers in hybrid P2P networks. Requesting peers are categorized differently and a discrete-time Geo/Geo/1+ 1 queuing model is established with simultaneous multiple working vacations, waiting threshold N, and two types of servers with different service rates. The steady-state distribution of the system is obtained by using the matrix-geometric solution method, and performance measures such as average queue length, average delay, and total energy consumption of the two types of requesting peers are calculated. Numerical experiments are conducted to analyze the effects of different parameters on the performance measures. Finally, the optimal strategies and Nash equilibrium points of requesting peers are studied, which provide a theoretical basis to suppress “free-riding” behavior.