Capacity of interconnected ring communication systems with unique loop-free routing (Corresp.)

Abstract

{\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 as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33.3</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80</tex> percent 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.