The results of study of the multipath routing tensor model with the quality of service in telecommunication networks

Tensor approach, which is used in the article for the mathematical description of telecommunication systems, allowed us to formulate analytically conditions for ensuring the quality of service at the same time on two factors: the required transmission rate of traffic and the end-to-end delay. The model described is designed to solve routing problems, but can be adapted for other tasks traffic management and design of communication systems. The proposed solution is invariant with respect to the analyzed network structures, service disciplines, and traffic patterns. All these features affect only the dimension and content of metric tensor and the coordinate transformation matrices. The main object of the study were selected tasks multipath routing. In this regard, the article made modeling and comparative analysis of the proposed and previously known solutions for key indicators of quality of service. The results of numerical analysis demonstrated the advantages of the tensor approach to the modeling of routing problems, which manifested itself in improving the multipath end-to-end delay, the probability of timely delivery of packets and jitter.