In wireless networks, the bitrate received by a user session depends not only on the fraction of allocated resources of the base station but also on the number of factors affecting the signal-to-noise ratio. These factors include a distance between a mobile device and the base station, walls, buildings between them, etc. As a result, the bitrate of elastic sessions may differ tenfold. In this paper, we develop a probabilistic model that captures the main specifics of the data transmission through a wireless network by introducing the random serving rate coefficients concept. With the help of the model, we derived the cumulative distribution function of the elastic session duration. © 2021 Institute of Physics Publishing. All rights reserved.