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In this paper, we consider a multi-traffic network system for next generation communication networks with a transmission link shared by an available bit rate (ABR) application for non-real time traffic and a Variable Bit Rate (VBR) application for real time traffic. Furthermore, an ABR traffic feedback controlling flow (TFCF) method is proposed to control the flow of the ABR traffic for multi-traffic networks. In TFCF, we discuss the performance of system. The two main objectives of queue management: high link utilization and low packet loss probability, are often in conflict. This paper intends to address these issues and offers analytical framework on how to ensure performance regardless of the concrete type of network. By the performance analysis, we establish a new tractable performance model for the network system. Then, based on simulation, the impact of several parameters on the system performance is presented through some numerical results.