Measures of Node

Quorum-based protocols can be formalized in terms of the data structures they use. These data structures, called quorum structures, include quorum sets, coteries, and bicoteries. Traditionally, weighted voting has been used to construct quorum structures. In order to obtain better performance, several researchers have proposed methods that impose a logical structure on the nodes. We have shown that these methods can be generalized by using composition. Several measures have been proposed to analyze quorum structures, including availability , communication latency, expected number of operational nodes, quorum size, node and edge vulnerability, reliability, and success rate. However, none of these measures can be used to measure the relative importance of each node in a quorum structure. In this paper, we present such a measure, called the Banzhaf index. By knowing the relative importance of each node in the system, it is possible to improve the overall system reliability by investing more eeort on improving the reliability of important nodes. Secondly, it is frequently not possible to compute these measures directly for a quorum structure in a large system. However, we present a simple recursive method to compute the importance of nodes in quorum sets constructed by using composition. Finally, we propose a new measure that can be used to evaluate the importance of each node in a bicoterie, and show that if the bicoterie is nondominated, this measure reduces to nding the importance of each node in a quorum set. We prove the correctness of our recursive methods and show that they are very eecient.