An Investigation into Transport Protocols and Data Transport ...

5.4. Analysis of AIMD Congestion Control 108
term is derived from the congestion measure 5 p i (t) and a drop of half from
the peak cwnd value of 4 3 w i(t).
It can be shown that Equation 5.9 readily reduces to Equation 5.8 when
w˙
i (t) = 0.
By defining that:
κ i (T i ) = 1 T i
and u i (w i (t), T i (t)) = 3
2w 2 i
(5.10)
[JDXW03] stipulate that all the design of congestion algorithms can be
generalised by the following:
ẇ = κ i (t) ×
(
1 − p )
i(t)
u i (t)
(5.11)
where κ(t) := κ(w i (t), T i (t)) and u(t) := u(w i (t), T i (t)) and is defined as
the gain function and the marginal utility function respectively.
By choosing an appropriate value of u(t) which is equivalent to the loss
probability, the time variance of w i can be minimised and therefore enable a
more ‘stable’ flow. Meanwhile, the choice of κ(t) facilitates a quick adaptation
to the equilibrium value of w.
Therefore, the choice of the variables κ(t) and u(t) play an important
role in the stability and responsiveness, and the equilibrium properties respectively.
5 Which for this discussion is equivalent to the the indication of packet loss.