  This paper investigates the problem of distributed medium access control in a
time slotted wireless multiple access network with an unknown finite number of
homogeneous users. Assume that each user has a single transmission option. In
each time slot, a user chooses either to idle or to transmit a packet. Under a
general channel model, a distributed medium access control framework is
proposed to adapt transmission probabilities of all users to a value that
maximizes an arbitrarily chosen symmetric network utility. Probability target
of each user in the proposed algorithm is calculated based upon a channel
contention measure, which is defined as the success probability of a virtual
packet. It is shown that the proposed algorithm falls into the classical
stochastic approximation framework with guaranteed convergence when the
contention measure can be directly obtained from the receiver. On the other
hand, when the contention measure is not directly available, computer
simulations show that a revised medium access control algorithm can still help
the system to converge to the same designed equilibrium.
