Performance analysis of P2P network with dynamic changes of servers based on M/M/c queuing model

Peer-to-Peer (P2P) network, which is distributed application architecture, distributes tasks and workloads among peers. One of most characteristics of P2P network is that peers play dual roles as servers and clients. To study the interaction process of nodes in P2P systems dynamically, the download delay of nodes, the energy consumption of the system and simulate the behavior of peers, analyze the performance of the P2P network, we develop an M/M/c queuing model with dynamic changes of servers, impatient customers and fault repairable. Using the quasi-birth-and-death process (QBD), the geometric solution of the matrix for the steady-state probability vector is derived. Since the matrix is quite complex, approximate solutions of the matrix equations are obtained using the Gauss–Seidel method, the performance indicators of the system are obtained. By employing Nash equilibrium and social optimal strategy, the optimal value of social benefits is obtained, which provides a theoretical basis and decision evaluation for scheduling of the nodes in the P2P system.