A Systematic Construction of Instability Bounds in LIS Networks

In this work, we study the impact of dynamically changing link slowdowns on the stability properties of packet-switched networks under the Adversarial Queueing Theory framework. Especially, we consider the Adversarial, Quasi-Static Slowdown Queueing Theory model, where each link slowdown may take on values in the two-valued set of integers {1, D} with D> 1 which remain fixed for a long time, under a (w, ρ)-adversary. In this framework, we present an innovative systematic construction for the estimation of adversarial injection rate lower bounds, which, if exceeded, cause instability in networks that use the LIS (Longest-in-System) protocol for contention-resolution. In addition, we show that a network that uses the LIS protocol for contention-resolution may result in dropping its instability bound at injection rates ρ> 0 when the network size and the high slowdown D take large values. This is the best ever known instability lower bound for LIS networks