A simplified description of communication networks

The paper proposes a simplified description for a network of $N$ points with transit paths whereby the computation of failure probability is simpler than in a comparable Markov mode. Asymptotic expressions are found for failure probabilities and median fractions of busy lines in bunches between any two points when the number of channels in such bunches increases infinitely with fixed loads on channel, $\{\alpha\}$, below 1. It is shown that the effectiveness of transits at $\{\alpha\}<1$ first drops with increasing number of channels in the bunches and then grows and that this effectiveness increases with $N$ if $\{\alpha\}$ smaller than a certain critical load.