Due to the limited bandwidth of wireless networks, an efficient medium-acce
ss control protocol is essential to meet the growing demand of wireless acc
ess. Most multiple-access protocols require contentions (collisions) in the
process of acquiring the transmission medium. While collisions cannot be a
voided, successive collisions that consist of the same group of active stat
ions are totally unnecessary, Successive collisions not only waste bandwidt
h, but also raise the concern of saturation in the channel. In this paper,
we solve the problem of repetitive contentions involving the same set of st
ations by using the theory of finite projective planes, Due to the property
of single-point intersection for an arbitrary pair of sets in the finite p
rojective plane, we can minimize the number of unnecessary collisions. Prot
ocol finite projective plane-based medium access control (FMAC) is highly f
lexible and has many features including adaptation for a mobile environment
, support for priority assignment and handoffs in cellular networks, and ex
tension of asynchronous transfer mode (ATM) services to mobile users, A per
formance evaluation shows that the throughput of the system is higher than
that of slotted ALOHA. By dynamically adjusting the retransmission probabil
ity and the order of the finite projective plane, protocol FMAC can be stab
ilized.