Fairness-Constrained Maximum Sum Rate of Multi-Rate CSMA Networks

This paper presents the sum rate analysis of a saturated M-group multi-rate carrier sense multiple access network, where nodes in different groups have distinct packet transmission rates. An explicit expression of the network sum rate is derived, based on which the maximum sum rate is obtained by optimizing the transmission probabilities of nodes. It is found that to achieve the maximum sum rate, only the group of nodes with the largest transmission rate is allowed to access the channel, which leads to severe unfairness. To ensure certain fairness, two constraints, namely, throughput fairness (TF) and data-rate fairness (DF), are proposed, with which each node acquires a target proportion of the network throughput and the network sum rate, respectively. Explicit expressions of the network maximum sum rate with TF and DF are derived, which show that by including the fairness constraints, the network maximum sum rate becomes inferior to that without fairness constraints as long as there is difference in the transmission rates of nodes. The analysis is further applied to IEEE 802.11 networks, where the optimal initial backoff window sizes of nodes to achieve the network maximum sum rates with both fairness constraints are derived.