A Markov model for carrier sense multiple access in coded wireless packet networks

We introduce a Markov model for the wireless broadcast advantage in carrier sense multiple access networks. The model uses a channel access Markov chain, which captures medium access and packet transmissions of all nodes, and a packet reception Markov chain, which accounts for successful reception or packet loss at all nodes within range jointly. The joint reception model is due to the shared wireless medium, where any packet transmission is naturally a broadcast. From this model, we derive the average information value of broadcasts, the so called broadcast function, which leads to the average achievable multicast throughput with network coding. Conditions for the feasibility of any given network coding subgraph, i.e., coded information flow, follow then immediately from the throughput equations. For sufficiently small information flow requirements, the necessary channel access rates can be easily determined by a suitable fixed point algorithm.