An optimal algorithm for mutual exclusion in computer networks

Abstract

An algorithm is proposed that creates mutual exclusion in a computer network whose nodes communicate only by messages and do not share memory. The algorithm sends only 2*(N - 1) messages, where N is the number of nodes in the network per critical section invocation. This number of messages is at a minimum if parallel, distributed, symmetric control is used; hence, the algorithm is optimal in this respect. The time needed to achieve mutual exclusion is also minimal under some general assumptions. As in Lamport's bakery algorithm, unbounded sequence numbers are used to provide first-come firstserved priority into the critical section. It is shown that the number can be contained in a fixed amount of memory by storing it as the residue of a modulus. The number of messages required to implement the exclusion can be reduced by using sequential node-by-node processing, by using broadcast message techniques, or by sending information through timing channels. The readers and writers problem is solved by a simple modification of the algorithm and the modifications necessary to make the algorithm robust are described.