Investigation of random access computer networks operating in a diffusion environment with an increasing number of subscriber stations

Abstract

Improving the performance of various types of communication networks in the modern world remains an urgent task, in connection with which research is underway to create hardware that expands the throughput of physical channels, new network protocols are being developed and existing network protocols are being modified, mathematical and computer modeling of data transmission mechanisms in communication networks is being carried out. The speed and reliability of data transmission over networks also depends on a number of factors, the nature of the influence of which is random. The combination of such factors is called a random environment. If the change in the states of the medium is continuous, then we speak of a diffusion medium. The object of the research is communication networks controlled by multiple access protocols and functioning in a random (diffusion) environment. The research tool for multiple access networks is the mathematical apparatus of the theory of finite-difference and differential equations, the theory of random processes and the theory of queuing. The proposed mathematical model of communication networks in a diffusion environment is investigated by an asymptotic method. The scientific novelty of the work lies in the fact that for the first time a mathematical model of a multiple access network operating in a diffusion environment was proposed and an asymptotic study was carried out. The asymptotic average of the normalized number of claims in the orbit (the source of repeated calls) and the deviation from this average are found, and the probability density of the values of the process of changing the number of claims in the orbit is obtained.