Packet Forwarding with Swaps

We consider packet forwarding in the adversarial queueing theory (AQT) model introduced by Borodin et al. In this context, a series of recent works have established optimal bounds for buffer space usage of O(log n) for simple network topologies, where n is the size of the network. Optimal buffer space usage, however, comes at a cost: any protocol that achieves o(n) buffer space usage cannot guarantee bounded packet latency. In this paper, we introduce a generalization of the AQT model that allows for packet swaps in addition to regular forwarding operations. We show that in this model, it is possible to simultaneously achieve both optimal buffer space usage and packet latency when the network is a path of length n. To this end, we introduce an analytic tool we call the smoothed configuration of the network. We employ the smoothed configuration to reason about packet latency for a large family of local forwarding protocols, whereby we derive our main result. We also employ the smoothed configuration to analyze the total buffer space usage of forwarding protocols under stochastic packet arrivals. We show that the total network load is n in its steady state, but that the system takes exponential time in expectation to reach a total load of n.