Mathematical models of data transmission process in telecommunication networks with control operations

The purpose of this work is to develop mathematical support for the design of the data transmission process based on the packet switching method, taking into account control operations determined by the functional dependence of the packet transmission time in telecommunication networks. Based on the packet switching method, the transmitted message at the source node was split into some packets that are transmitted along some routes to the destination node. On each route, control operations of transmitted packets and return messages or receipts (control of the correctness of transmitted packets on routes) were added. The time of control operations was determined by the functional dependence of the random variables of the packet transmission time of the corresponding routes. To obtain the distribution of the transmission time of control messages and the distribution of time on each route, it was proposed to use the theory of residues. On the basis of mathematical expressions, a method is proposed for finding the distribution of the start time of packet assembly at the recipient's node as the maximum of several random variables of the data transmission time. The obtained distribution density of data transmission time in networks allows calculating the distribution function of the packet assembly time at the receiver's node

1. Goldstein B.S. Switching systems. Textbook for universities. M.: BHV-Petersburg. 2004:316.

2. Roberts L.G. The evolution of packet switching. Proceedings of the IEEE. iss. on packet communication networks, no. 11 (November). 1978;66:1307-1313.

3. Berlin A.N. Switching in communication systems and networks. M.: Eco-Trends. 2006:344.

4. Vasin N.N. Packet switching technologies: Textbook. St. Petersburg: Lan. 2019:284.

5. Mizn I.D., Bogatyrev V.A., Kuleshov A.P. Packet switching networks. M.: Radio and communication. 1986:410.

6. Abilov A.V. Communication networks and switching systems: Textbook. Manual for universities. M.: Radio and communication. 2004:288.

7. Knyazeva G.V. Bulletin of the Volga University them V.N. Tatishcheva. Study of problems combining technologies of ethernet and atm in the construction of local networks. 2011;17:140-150.

8. Volkhonsky V., Volkovitsky V. Digital TV surveillance systems. Safety. Credibility. Information. 2009;85:38-47.

9. Mishin V.A., Ryzhiy V.M. Selection of the optimal ratio of switching methods on the transport network. Technique & technology. 2012;3:41.

10. Phillips D., Garcia-Diaz A. Network analysis methods. M.: Mir. 1984:496.

11. Ventzel E.S., Ovcharov L.A. Probability theory and its engineering applications. M: Higher school. 2000:480.

12. Wentzel E.S. Probability theory. M.: Higher school. 1999:576.

13. Gnedenko B.V. Probability theory course. M.: Nauk. Ch. ed. physical -mat. lit. 1971:100