An Investigation into Transport Protocols and Data Transport ...

5.4. Analysis of AIMD Congestion Control 106
of the graph) provides the utilisation of the flow:
η = β2 (1 + γ) 2 − 2γ − 1
2(β − 1)(1 + γ)
(5.6)
As such, Equation 5.6 states that the utilisation of the link of capacity B
is dependent on the queue size provision γ and the back-off factor β of the
TCP flow only. This assumes that the only form of congestion signal is that
from the overflow of the buffer from this flow only (i.e. zero packet loss) and
that the number of congestion epochs experienced by the flow is sufficiently
large.
Therefore, substituting the default decrease parameter of 1 and a queue
2
provision of zero gives 75% utilisation of the bandwidth B. Similarly, with
a queue provision γ of 1 (i.e. q = BT , the Bandwidth Delay Product), the
flow will experience 100% utilisation with β = 1/2.
5.4.2 Response Function
Mathematical models of the evolution of a TCP flow have been developed in
order to provide researchers with tools to accurately design new models and
to modify new congestion control models.
One of the most popular is the response curve [PFTK00] that defines the
bulk transfer throughput of TCP Reno for different loss conditions. Unlike
previous models, Equation 5.7 predicts the throughput of TCP under both
timeouts and congestion avoidance and is given by,
B =
√ (
2p
T + T 3 0 3
s
√
)
3p
p(1 + 32p
8
2 )
(5.7)