Transmission control of two-user slotted ALOHA over Gilbert-Elliott channel: Stability and delay analysis

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 polygon 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 boundary of the stability region is characterized 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.