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 Queuing 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 obtain the following results:
• Allowing such dynamic changes to 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 and for large enough values of C.
• The combination of dynamically changing link capacities with compositions of contention–resolution protocols on network queues suffices for similar instability bounds: 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 for large enough values of C.
• The instability bound of the network subgraphs that are forbidden for stability is affected by the dynamic changes to the link capacities: we present improved instability bounds for all the directed subgraphs that were known to be forbidden for stability on networks running a certain greedy protocol.