K-Coterie and Coterie Join Operation

Abstract

In distributed systems, quorum-based algorithms are used to access shared resources in a mutually exclusive way because these algorithms are more resilient to process and communication failures. Based on resource allocation, the quorum system for the mutual exclusion problem is a coterie and the quorum system for the k-mutual exclusion problem is a k-coterie. There are two types of coteries and k-coteries which are dominated and nondominated. The availability of a coterie and a k-coterie need to be considered in an error-prone system. Therefore, k-coterie and coterie join operation is presented to build a new larger k-coterie so that the availability of a k-coterie increases. Through an analysis of availability is obtained that a k-coterie C is nondominated if and only if for any probability p, the sum of the (k,1)-availability and the (k, k)- dual availability of a coterie C equals one.