The robustness of stability under link and node failures

Abstract

In the area of communication systems, stability refers to the property of keeping the amount of traffic in the system always bounded over time. Different communication system models have been proposed in order to capture the unpredictable behavior of some users and applications. Among those proposed models the adversarial queueing theory (AQT) model turned out to be the most adequate to analyze an unpredictable network. Until now, most of the research done in this field did not consider the possibility of the adversary to produce failures on the network structure. The adversarial models proposed in this work are inspired by the AQT model, but incorporating the possibility of dealing with node and link failures provoked by the adversary. Such failures produce temporal disruptions of the connectivity of the system and increase the collisions of packets in the intermediate hosts of the network, and thus the average traffic load. Under such a scenario, the network is required to be equipped with some mechanism for dealing with those collisions. In addition to proposing adversarial models for faulty systems we study the relation between the robustness of the stability of the system and the management of the queues affected by the failures. When the adversary produces link or node failures the queues associated to the corresponding links can be affected in may different ways depending on whether they can receive or serve packets or they can not. We show that, in most of the cases, very simple network topologies and protocols, which were known to be universally stable, i.e. stable under any allowed configuration of the system, in the AQT model, turn out to be unstable when considering some of the newly proposed adversarial models. Thus showing that in general stability is not a robust property in the presence of failures.