The increase of the instability of networks due to Quasi-Static link capacities

In this work, we study the impact of the dynamic changing of the network link capacities on the stability properties of packet-switched networks. Especially, we consider the Adversarial, Quasi-Static Queueing Theory model, where each link capacity may take on only two possible (integer) values, namely 1 and C > 1 under a (w, ρ)-adversary. We show that allowing the dynamic changing of the link capacities of a network with just ten nodes that uses the LIS (Longest-in-System) protocol for contention-resolution results in instability at rates ρ > √ 2− 1 for large enough values of C. The combination of dynamically changing link capacities with compositions of contention-resolution protocols on network queues suffices to drop the instability bound of a network to a substantially low value. We show that the composition of LIS with any of SIS (Shortest-in-System), NTS (Nearest-to-Source) and FTG (Furthest-to-Go) protocols is unstable at rates ρ > √ 2−1 for large enough values of C. We prove that the instability bound of the network subgraphs that are forbidden for stability is affected by the dynamic changing of the link capacities presenting improved instability bounds for all the directed subgraphs that are known to be forbidden for stability on networks running a certain greedy protocol.