  In this paper, we consider the problem of calculating the stability region
and average delay of two user slotted ALOHA over a Gilbert-Elliott channel,
where users have channel state information and adapt their transmission
probabilities according to the channel state. Each channel has two states,
namely, the 'good' and 'bad' states. In the 'bad' state, the channel is assumed
to be in deep fade and the transmission fails with probability one, while in
the 'good' state, there is some positive success probability. We calculate the
Stability region with and without Multipacket Reception capability as well as
the average delay without MPR. Our results show that the stability region of
the controlled S-ALOHA is always a superset of the stability region of
uncontrolled S-ALOHA. Moreover, if the channel tends to be in the 'bad' state
for long proportion of time, then the stability region is a convex Polyhedron
strictly containing the TDMA stability region and the optimal transmission
strategy is to transmit with probability one whenever the nodes have packets
and it is shown that this strategy is delay optimal. On the other hand, if the
channel tends to be in the 'good' state more often, then the stability region
is bounded by a convex curve and is strict subset of the TDMA stability region.
We also show that enhancing the physical layer by allowing MPR capability can
significantly enhance the performance while simplifying the MAC Layer design by
the lack of the need of scheduling under some conditions. Furthermore, it is
shown that transmission control not only allows handling higher stable arrival
rates but also leads to lower delay for the same arrival rate compared with
ordinary S-ALOHA.
