Availability of k-coterie

The distributed k-mutual-exclusion problem (k-mutex problem) is the problem of guaranteeing that at most k processes at a time can enter a critical section at a time in a distribution system. A method proposed for the solution of the distributed mutual exclusion problem (i.e., 1-mutex problem) by D. Barbara and H. Garcia-Molina (1987) is an extension of majority consensus and 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: the network topology is a complete graph, the links never fail, and p, the reliability of the process, is at least 1/2. The concept of a k-coterie, an extension of a coterie, is introduced for solving the k-mutex problem, and lower and upper bounds are derived on the reliability p for k-majority coterie, a natural extension of majority coterie, to be optimal, under conditions (1)-(3). For example, when k=3, p must be greater than 0.994 for k-majority coterie to be optimal