An O(NM(M+1/)) distributed algorithm for the k-out of-M resources allocation problem

This paper presents a permission-based algorithm to solve the problem of M identical resources shared among N processes in a distributed system. We prove that the number of messages exchanged necessary for a process to acquire k resources is O(N^M(M+1)/). This result has been obtained (i) investigating the concept of arbiter of conflicting processes and (ii) extending conditions that permit conflict detection and resolution in a system of N competing processes to M shared resources. We show that for M=1 we get Maekawa´s algorithm. However, we will also show that Maekawa´s results, being based on finite projective plane geometry, do not apply for M>1