Asymptotic Approach to the Investigation of Message Switching Networks of Linear Structure with a Large Number of Nodes

The article examines message switching networks of linear structure with a large number of nodes at which messages arrive and are received. Under the assumption that the loading of the network is low, the existence of a limiting process of message arrival as $\mathscr N\to\infty$ and $t\to\infty$ is demonstrated ($\mathscr N$ being the number of a node in a linear network and $t$ the time).