Dynamic and static packet routing on symmetric communication networks

For dynamic routing on any vertex and edge symmetric topology we relate network contention to the packet generation rate, and the degree and average distance of the underlying topology. As a direct consequence we show that the star graph becomes saturated as the packet generating rate approaches one. Also, for graphs of approximately the same order, the average delay of a packet routed on an alternating-group graph is smaller than the corresponding delays on the hypercube and the star graph. Similar conclusions are drawn from comparisons based on various static permutation routing problems. Our theoretical results compare favorably with simulations of considerably large systems.