  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.
