Local Diffusion Approximation of the State Changing Process of an Unstable Random Access Network in a Neighborhood of the Asymptotic Mean

A mathematical non-Markovian model of an unstable random access network is investigated by the asymptotic analysis method. A random process is constructed which approximates the values of deviations of the normalized number of messages from the asymptotic mean. This process is shown to be Gaussian; explicit expressions for its drift coefficients, diffusion, and other characteristics are obtained.