Simple routing strategies for adversarial systems

In this paper we consider the problem of delivering dynamically changing input streams in dynamically changing networks where both the topology and the input streams can change in an unpredictable way. In particular, we present two simple distributed balancing algorithms (one for packet injections and one for flow injections) and show that for the case of a single receiver these algorithms will always ensure that the number of packets or flow in the system is bounded at any time step, even for an injection process that completely saturates the capacities of the available edges and even if the network topology changes in a completely unpredictable way. We also show that the maximum number of packets or flow that can be in the system at any time is essentially best possible by providing a lower bound that holds for any online algorithm, whether distributed or not. Interestingly, our balancing algorithms do not only behave well in a completely adversarial setting. We show that also in the other extreme of a static network and a static injection pattern the algorithms will converge to a point in which they achieve an average routing time that is close to the best possible average routing time that can be achieved by any strategy. This demonstrates that there are simple algorithms that can be efficient for very different scenarios.