Impact of Time-based Fairness

Under the time-based fairness, our proposed definition of fairness, each node achieves an equal share of channel occupancy time. Thus,

$$T'(i) = \frac{1}{n}$$ (11)

Substituting Equation 11 in Equations 2 and 3,

$$R'(i) = \frac{\gamma_i}{n}$$ (12)

$$R'(I) = \frac{1}{n} \sum_{i \in I}{\gamma_i}$$ (13)

Notice that R'(i) only depends on what node i can achieve under the given conditions and the number of competing nodes. It does not depend upon the data rates or packet sizes used by competing nodes. Unlike R(I) shown in previous subsections, R'(I) is a simple summation of each node's maximum achievable throughput when all competing nodes use its data rate and packet size. R'(I), and R(I) in Equations 7 and 10 will be equal if and only if all nodes in I use the same data rate and packet size.

Table 2: The experimentally achieved total throughput (or the baseline throughput) of the two nodes simultaneously exchanging data at the same data rate d and packet size s. Each node has a similar frame loss rate of less than $2\%$.

d ( Mbps)	s (Byte)	n = |I|	$\gamma(d, s,I)$
11	1500	2	5.189
5.5	1500	2	3.327
2	1500	2	1.493
1	1500	2	0.806

Table 3: Comparison of achieved throughputs (in Mbps) of four nodes, each transmitting at 1, 2, 11 and 11 Mbps respectively, under RF and TF. Note that R(n1) under TF is the same as what n1 would achieve if all n2, n3 and n4 transmit at 1 Mbps.

Fairness	R(n1)	R(n2)	R(n3)	R(n4)	Total
Criteria	(1)	(2)	(11)	(11)
RF	0.436	0.436	0.436	0.436	1.742
TF	0.202	0.373	1.30	1.30	3.175