Stability of adaptive and nonadaptive packet routing policies in adversarial queueing networks

We investigate the stability of packet routing policies in adversarial queueing networks. We provide a simple classification of networks which are stable under any greedy scheduling policy. We show that a network is stable if and only if the underlying undirected connected graph contains at most two edges. We also propose a simple and distributed policy which is stable in an arbitrary adversarial queueing network even for the critical value of the arrival rate r = 1. Finally, a simple and checkable network flow-type load condition is formulated for adaptive adversarial queueing networks, and a policy is proposed which achieves stability under this new load condition. This load condition is a relaxation of the integral network flow-type condition considered previously in the literature.