Analysis of a Fully Connected Message-Switching Communication Network with a Large Number of Nodes, Bypass Routes, and a Limited Number of Waiting Places at Nodes

The author obtains the asymptotic values as $N\to\infty$ of some characteristics of a fully connected message-switching network with $N$ nodes, bypass routes, and a limited number of waiting places at nodes. It is shown that there is a “phase transition of the first kind” in the network as $N\to\infty$. The interrelationship between the phase transition and purposeful load-limiting discipline as $N\to\infty$ is considered. The results are obtained under the assumption that as $N\to\infty$ the queues at the nodes are statistically independent and can be approximated by queues in $M|M|1$ queuing systems with a limited number of waiting-places and with intensities of the incoming flows determined from the self-consistency conditions.