Optimal Node Routing

We study route selection for packet switching in the competitive throughput model. In contrast to previous papers which considered competitive algorithms for packet scheduling, we consider the packet routing problem (output port selection in a node). We model the node routing problem as follows: a node has an arbitrary number of input ports and an arbitrary number of output queues. At each time unit, an arbitrary number of new packets may arrive, each packet is associated with a subset of the output ports (which correspond to the next edges on the allowed paths for the packet). Each output queue transmits packets in some arbitrary manner. Arrival and transmission are arbitrary and controlled by an adversary. The node routing algorithm has to route each packet to one of the allowed output ports, without exceeding the size of the queues. The goal is to maximize the number of the transmitted packets. In this paper, we show that all non-refusal algorithms are 2-competitive. Our main result is an almost optimal e e−1 ≈ 1.58-competitive algorithm, for a large enough queue size. For packets with arbitrary values (allowing preemption) we present a 2-competitive algorithm for any queue size.