Throughput modeling of single hop CSMA networks with non-negligible propagation delay

We analyze the performance of the CSMA protocol under propagation delays that are comparable with packet transmission times. We propose a semi-Markov model for the 2-node CSMA channel. For the 2-node case, the capacity reduces to 40% of the zero-delay capacity when the one-way propagation delay is 10% of the packet transmission time. We then extend this model and obtain the optimum symmetric probing rate that achieves the maximum network throughput as a function of the average propagation delay, d, and the number of nodes sharing the channel, N. The proposed model predicts that the total capacity decreases with d-1 as N goes to infinity when all nodes probe the channel at the optimum rate. The optimum probing rate for each node decreases with 1/N and the total optimum probing rate decreases faster than d-1 as N goes to infinity. We investigate how the short-term unfairness problem in CSMA worsens as the propagation delay increases and propose a back-off mechanism to mitigate this issue. The theoretical results presented in this paper can be used as a benchmark for the performance improvements provided by algorithms that have already been developed.