When optimal minimum CW is chosen according to (34) or (35), the ratio of bits transferred per node for slow and fast station becomes equal to unity, thus resulting in bit-based fairness.
Since the fairness index F becomes equal to unity when z S = z M = z F, where z i (i = S, M, F) represent the bits transferred per node for slow, medium and fast nodes respectively.
Recall that the fairness index F becomes equal to unity when the bits transferred per node for slow and fast nodes are equal; i.e., z S = z F. From (28), we have ( 1 - p c, S ) ( 1 - τ S ) = ( 1 - p c, F ) ( 1 - τ F ) = ( 1 - τ S ) n S ( 1 - τ F ) n F. Assume WS,min, WF,min>> 1 and τ S, τ F << 1 so that pc,S≅ pc,F.
I wish us to become equal to ourselves.
Nor do human beings become equal to God.
For r1 → ∞ (i.e. r c → ∞ or r a → 0), S (T s ) becomes equal to T s, represented by a straight line with a slope of unity (the left, upper bound).
For the usual vibration isolation control systems, the maximum transmissibility is greater than or equal to unity, while when the present method is used the transmissibility becomes less than 20percentt of the external disturbance for a practical system with friction.
For odd M, this distribution become the Erlang's one [39] with the shape parameter δ p and the scale parameter equal to unity.
Precisely, the transmission coefficient is almost equal to unity for the all studied cases.
