On the availability of k-coteries in networks with unreliable nodes and links

The use of a k-coterie (a special set of subsets of nodes) is known as a robust approach to solving the distributed k-mutual exclusion problem in distributed systems. In order to evaluate the fault-tolerance capability of k-coterie-based methods, the notion of (k, τ) availability has been proposed as a generic measure. However, the applicability of the only existing evaluation method is limited to systems such that the nodes are fully connected by completely reliable links. To overcome the limitation, we propose a new method that can evaluate the (k, τ)-availability of k-coteries in general topology networks with unreliable nodes and links. The proposed method uses a new notion called minimal quorum spanning forests to perform evaluation effectively. Using the method, we find that the k-majority coterie, which is optimal when the network is completely reliable, is not necessarily optimal if the links can fail and/or the system has a topology other than a complete graph