Resource Loss Systems and Performance Analysis of Wireless Networks
Mathematical analysis plays an indisputable role in almost all spheres of human activity. The world public telecommunications network is the largest technical object that a human has ever built. This network has been created since about the end of the 19th century and has survived all the stages of the development of industrial society. By 2020, 5 generations of the telecommunication network have already been created, and the scientific community is already discussing the networks of the future 6th generation of the network. At all stages, starting from the tasks set by the outstanding mathematicians Agner Erlang and Aleksandr Khinchin, engineers turned to various mathematical theories and methods both to evaluate the performance of existing networks as well as to build models of future systems, even those that have not yet passed the laboratory research stage. Almost no scientific article devoted to the R&D of telecommunication systems and networks is complete without the construction of mathematical models and their mathematical analysis. The created methods in some cases served the development of purely mathematical disciplines such, as queuing theory, coding theory, and some others.
We devote this keynote to the problems of the application of mathematical analysis in telecommunications and base it on the book «Matrix and analytical methods for performance analysis of telecommunication systems» dedicated to our teacher Gely Basharin and written by Valeriy Naumov, Yuliya Gaidamaka, Natalia Yarkina, Konstantin Samouylov. Of course, it is impossible in one speech to even briefly outline a book that describes the research of RUDN University mathematicians for about 60 years. The presentation will be focused on the part where the evolution of models is sequentially presented, starting from the famous Erlang formula, and up to the Resource Loss Systems we have built, aimed at analyzing new generations of wireless networks.