## 4 Computational Experiments
### Efficiency of the Algorithm on Problems of Higher Dimension  
Communication networks, including satellite ones, are becoming more complex. In this regard, the behavior of the prepositional algorithm and the time it takes for more cumbersome network topologies is interesting. Comparison with known methods in this case is difficult due to their unacceptable computational complexity. Therefore, in this subsection the behavior of the algorithm is studied depending on the complexity of the problems being solved. For the experiments, a computer with the following characteristics was used: CPU Intel Core i5-12400F, RAM: DDR5, 32 GB, 4800 MHz, motherboard: Gigabyte B760M DS3H. Only one processor core was used. The algorithm efficiency was estimated as follows: calculations for each version of the initial data were repeated 10 times and the results were averaged. The tested topologies were randomly generated with the following parameters: the number of nodes was 100, with an average of 20 edges outgoing from each node. Let us define the network density as the ratio of the number of outgoing edges to the number of nodes. In our case, the density was 0.2. The buffer size of each channel was 50. The number of target requests varied from 10 to 100 in steps of 10. The request intensity changed from 1 to 50 in steps of 0.1. As a result, 4900 various data sets were generated. The entire modeling process can be divided into 10 parts; each part is characterized by a set of target queries from 10 to 100 in steps of 10. Thus, 490 experiments were generated within each part. All experiments can be divided into 2 parts: successful and unsuccessful. Successful experiments are those that resulted in the transfer of the entire planned amount of data required by the target requests. Each target request varied from 1 to 50 packets per second in steps of 0.1. The numbers of pairs of source and receiver nodes were randomly generated for each request. Figure 7 shows the second part, in which 20 requests were transmitted. As can be seen from the graphs, the execution time of the algorithm for finding the optimal distribution varies in proportion to the number of routes involved. An abrupt change in the number of routes corresponds to an abrupt change in the calculation time. It is also seen from Figure 8 that the maximum achievable request intensity is up to 28.1 packets per second. When it reaches a maximum of 50 packets/second during the experiment (Figure 7), this value corresponds to experiment 762 in Figure 7 and the extreme point. Note that the maximum number of routes at which the possibility of transmitting all the data is granted does not exceed 23. This means that the generated topology and the selected sender and recipient nodes for each request are not selected in the most successful places in the topology. Since at least 20 routes are required to transmit data for 20 requests, in this case this means that only three additional routes were found, along which some of the requests managed to redistribute information flows. Figure 7 shows that with an increase in the intensity of requests, the algorithm managed to find 37 alternative routes for all requests. However, it was not possible to deliver all the required information to recipients, as can be seen after experiment 762. Note that the criterion for stopping the algorithm was the objective function change at the next iteration not exceeding 10-8, if it finds a solution for transmitting all the traffic, or 40 iterations of the main algorithm if it is impossible to transmit the entire amount of information. Note that the authors followed certain goals for which this algorithm was developed, and these criteria for stopping were selected empirically for the problem being solved. Obviously, this criterion may not be suitable for all possible topological configurations and is the subject of further research. Figure 8: Modelling results for 20 target requests. Request intensity varies from 1 to 50 in steps of 0.1. Only results with granted transfer of all the requests are shown.