  We study the motion of a substance in a channel that is part of a network.
The channel has 3 arms and consists of nodes of the network and edges that
connect the nodes and form ways for motion of the substance. Stationary regime
of the flow of the substance in the channel is discussed and statistical
distributions for the amount of substance in the nodes of the channel are
obtained. These distributions for each of the three arms of the channel contain
as particular case famous long-tail distributions such as Waring distribution,
Yule-Simon distribution and Zipf distribution. The obtained results are
discussed from the point of view of technological applications of the model
(e.g., the motion of the substance is considered to happen in a complex
technological system and the obtained analytical relationships for the
distribution of the substance in the nodes of the channel represents the
distribution of the substance in the corresponding cells of the technological
chains). A possible application of the obtained results for description of
human migration in migration channels is discussed too.
