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The QoS solution of traffic management based on the dynamic tensor model in the coordinate system of interpolar paths and internal node pairs is presented. The conditions of ensuring QoS-routing for different flows classes along multiple paths for the set of metrics as the packet rate and average packet end-to-end delay are expressed. The research results demonstrated that it is important to take into account the dynamics of network state changes in the conditions of high utilization of its interfaces, when the average packet end-to-end delay along the network paths behaves nonstationary.