A Markovian Analysis of an IEEE-802.11 Station with Buffering

The purpose of this paper is to analyze the so-called backoff tech- nique of the IEEE 802.11 protocol with buffers. This protocol rules the trans- missions on a radio channel between nodes (or stations) of a network exchanging packets of information. In contrast to existing models, packets arriving at a sta- tion which in the backoff state are not discarded, but are stored in a buffer of in nite capacity. The backoff state corresponds to the number of time-intervals (mini-slot) that a node must wait before its packet is actually transmitted. As in previous studies, the key point of our analysis hinges on the assumption that the time on the radio channel is viewed as a random succession of trans- mission slots (whose duration corresponds to a packet transmission time) and mini-slots, which stand for the time intervals during which the backoff of the station is decremented. During these mini-slots the channel is idle, which im- plies that there is no packet transmission. These events occur independently with given probabilities, and the external arrivals of messages follow a Pois- son process. The state of a node is represented by a three-dimensional Markov chain in discrete-time, formed by the triple (backoff counter, number of packets at the station, number of transmission attempts). Stability (ergodicity) condi- tions are obtained for an arbitrary station and interpreted in terms of maximum throughput. Several approximations related to these models are also discussed.