## 5 Conclusions  
In this paper, we proposed a heuristic greedy-gradient route searching method to find the optimal distribution of traffic in telecommunication networks according to loss-minimizing criteria. This algorithm is capable of finding data transmission routes for the initial set of target requests and to distribute all network traffic among them according to the criterion of minimizing losses. To solve this problem, the Floyd-Warshall algorithm is used, in which the derivatives of the loss functions in the channel corresponding to each edge are used as the weights of the directed graph. Accordingly, the problem of traffic distribution along the resulting routes is solved. The algorithm finds the same optimum regardless of the starting point of descent in the new search space. Despite the inaccuracies in calculating derivative estimates, the solution obtained is very close to the optimum in terms of the value of the objective function. When solving high-dimensional test tasks, the developed algorithm is approximately 10,000 times faster than the coordinate descent algorithm in the new search space and at the same time corresponds to it in terms of the accuracy of the results obtained within 1%. A feature of our new algorithm is the need to know the number of routes required to solve the optimization problem, which makes it similar to greedy algorithms and brings it closer in speed to them. On the other hand, computing pseudoderivatives to iteratively compute graph weights makes it akin to gradient algorithms. Another feature of this approach is that there is no need to explicitly compose the objective function and the constraints, as is required by streaming algorithms. In fact, the new algorithm solves a constrained optimization problem with a large number of equality-type constraints, which makes it difficult to solve by gradient methods. In the proposed approach, the constraints are taken into account when calculating the weight coefficients. The considered example of modeling on a network of 100 nodes with a density of 0.2 demonstrates the capability of our new algorithm to simulate data transfer processes  
Figure 11: Change in calculation time and the number of total number of routes when the condition of the 3 rd mode is met. \(M1^{<3>}\) (red): number of target requests, \(M1^{<7>}\) (blue): number of routes, \(M1^{<8>}\) (black): calculation time. in real time, both during preliminary modeling and in communication network control systems. In this example, the largest number of target requests was equal to the number of nodes (each network node was assumed to be a source of information). Using mass-market computer equipment for such a network, the worst-case simulation took approximately 70 ms. The quality of the resulting solution ensured the delivery of all information. For overloaded networks, when it is impossible to find routes that ensure the delivery of all data the operating time of the algorithm did not exceed 340 ms, which is also quite acceptable. In total, we carried out approximately 5000 experiments with the new algorithm, and the resulting time costs allow us to assert that the new algorithm is capable of effective modeling and control of any type of network due to the higher rate of operation of the algorithm compared to the rate of topology changes. Our new algorithm is heuristic and does not guarantee the global optimality of the results. However, further research aimed at analyzing and clarifying the stopping criteria of the algorithm depending on the network structure seems to be promising and may further reduce the computation time. The use of the derivative of the loss probability function as a communication-channel metric in dynamic routing protocols depending on the state of the communication channel also seems promising, since preliminary experiments in this direction have shown good results. Conceptualization, K.G., D.T. and S.K. ; methodology, K.G. and L.K. ; software, D.T. ; validation, K.G., L.K., D.M. and A.P. ; formal analysis, N.S. ; investigation, D.T. and D.M.