Impact of Rate Diversity

To understand the impact of rate diversity, let's assume that each node uses the same packet size, i.e. $\forall i,j \in I$, s_i = s_j. Therefore, based on Equations 2 and 3,

$$T(i) = \frac{\frac{1}{\gamma_i}}{\sum_{j \in I}{\frac{1}{\gamma_j}}}$$ (5)

$$R(i) = \frac{1}{\sum_{j \in I}{\frac{1}{\gamma_j}}}$$ (6)

$$R(I) = \frac{n}{\sum_{j \in I}{\frac{1}{\gamma_j}}}$$ (7)

Equation 6 clearly shows that the throughput of each node i is the same. Thus, under these conditions, DCF achieves throughput-based fairness. Observe, however, the amount of throughput is dependent on the baseline throughputs of all nodes in I, which in turn depend on their data rates and packet sizes.

The channel occupancy time T(i) of node i is inversely proportional to the baseline throughput of node i, which increases with the increase in transmission rate. Thus, as expected, nodes with slower data rates occupy the channel much longer than those with higher data rates, leading to degradation in the overall network performance.