Dynamic Sharing of a Multiple Access Channel

In this paper we consider the mutual exclusion problem on a multiple access channel. Mutual exclusion is one of the fundamental problems in distributed computing. In the classic version of this problem, $n$ processes perform a concurrent program which occasionally triggers some of them to use shared resources, such as memory, communication channel, device, etc. The goal is to design a distributed algorithm to control entries and exits to/from the shared resource in such a way that in any time there is at most one process accessing it. We consider both the classic and a slightly weaker version of mutual exclusion, called $\ep$-mutual-exclusion, where for each period of a process staying in the critical section the probability that there is some other process in the critical section is at most $\ep$. We show that there are channel settings, where the classic mutual exclusion is not feasible even for randomized algorithms, while $\ep$-mutual-exclusion is. In more relaxed channel settings, we prove an exponential gap between the makespan complexity of the classic mutual exclusion problem and its weaker $\ep$-exclusion version. We also show how to guarantee fairness of mutual exclusion algorithms, i.e., that each process that wants to enter the critical section will eventually succeed.