Availability of k-Coterie

The distributed k-mutual exclusion problem (kmutex problem) is the problem of guaranteeing that at most k processes can enter a critical section at a time in a distributed system. The distributed mutual exclusion problem (i.e., 1-mutex problem) is considered as one of the most fundamental distributed problems and several methods have been proposed for solving it. One of such methods, which is proposed by Barbara and Garcia-Molina as an extension of majority consensus, uses coteries. The goodness of coterie based 1-mutex algorithm strongly depends on the availability of coterie, and it has been shown that majority coterie is optimal in this sense, provided that 1) the network topology is a complete graph, 2) the links never fail, and 3) p, the reliability of process, is at least 1/2. This paper introduces the concept of a k-coterie as an extension of a coterie for solving the k-mutex problem, and derives a lower and an upper bounds on the reliability p for k-majority coterie, a natural extension of majority coterie, to be optimal, under the same conditions l)-3). For example, when k = 3, p must be greater than 0.994 for k-majority coterie to be optimal.