A new analytic approach for the performance evaluation of buffer insertion rings is proposed which overcomes the basic limitations of former analyses. Key to our analysis is that the global performance model of a buffer insertion ring is decomposed into submodels in such a way that the basic interdependence of interarrival and transmission times of the frames transmitted is taken into account. The analysis itself is relatively straightforward and yields simple and explicit results for the mean delays of the frames. For special traffic patterns, the analysis is exact, for the general case, it is approximate but its accuracy turns out to be high, as comparison with simulation results shows.

{\em Capacity} is defined for a given distribution of offered traffic as the maximum rate with which packets can be sent with finite delay through the network by appropriate routing. It is shown how capacity depends on the traffic characteristics and on the topology of ring communication systems interconnected so as to provide unique loop-free routing. First, the traffic conditions are given under which the capacity of a {\em single ring} attains its maximum and its minimum. For the case of {\em uniform traffic} it is shown that the capacity is equal to twice the minimum capacity. Then it is shown that, for uniform traffic, the capacity relative to a single ring communication system can be increased by as much as33.3or80percent when the stations are split up into two or three separate rings, respectively, interconnected to give unique loop-free routing. Exact formulas are given for the capacity of systems with an arbitrary number of stations split up into an arbitrary number of separate rings interconnected to give unique loop-free routing. Finally, it is shown that connecting {\em local rings} through a star network with a central switching node is particularly useful when stations can be segregated into local groups of stations which often communicate with stations from the same local group but only rarely with stations from the other groups. Exact formulas are given to calculate the capacity of such interconnected ring communication systems.