Region based containers — A new paradigm for the analysis of fault tolerant networks

Network Fault Tolerance has classically focused on the connectivity of the underlying graph of the network. A k-connected graph will tolerate up to k-1 node or edge failures allowing the remaining nodes to still communicate between them. The introduction of ‘Containers’ of the underlying graph enabled the measurement of the graceful degradation of the remaining network with the removal of faulty nodes and edges. This metric was required to bound the diameter degradation of the network. Recently, another major metric ‘Region Based Connectivity’, was introduced to study the locality of the faults in network robustness, by studying the resilience of networks with the loss of regions instead of individual nodes. Since real life networks often have localized outages, it is important to study losses of regions at a time. In this study, we introduce a new concept called ‘Region Based Containers’ of graphs. This framework will enable the analysis of fault tolerant networks where the two paradigms are brought together to study the graceful degradation of networks when multiple regions are affected. In this paper we propose a framework for network QoS using Region Based Containers and its application to fault tolerant design of networks. We then describe an example of networks built by regular Extended Line Graphs and present tight bounds in network degradation with multiple region failures. In the example the diameter of these networks degrade by at most one, despite the failure of d-1 regions where d is the regular degree of the network. The upper bounds on the size of these regions is presented. This metric is especially applicable to networks where faults are either localized by nature, or faults tend to result in cascading errors in their vicinity, such as power distribution networks, server clusters, or in extreme environments where redundancy of paths is necessary rather than a bonus.