FIFO at arbitrarily low rates

It was stated in Lecture 4 that under an adversarial queueing model, FIFO can be made unstable at arbitrarily low rates, r. The class began with a presentation demonstrating this by an example. Earlier work [2], [5], [4], [6] had shown that FIFO is unstable at rates exceeding .85, .83, .749 and .5 respectively, under an adversarial queueing model. In [7] the authors show that an adversarial injection protocol with an arbitarily low rate r, for a network of size Õ( r ) can be constructed, that makes FIFO unstable. The central idea is to construct a network from a concatenation of gadgets that allow only a small fraction of packets to pass through them for a long duration, and to inject packets after delaying and synchronizing them so that at the end of each injection phase, the number of packets waiting to traverse an edge increases. The gadget described has 2k vertices and k edges, classified as input, output and load edges. There are two types of packet flows in this network gadget-traversing packets that enter from an input edge, traverse all the k load edges in order and then exit from the adjacent output edge, and internal-gadget packets that are traverse a single load edge.