An Investigation into Transport Protocols and Data Transport ...

5.4. Analysis of AIMD Congestion Control 104
k th congestion epoch
w i
(k)
k th congestion epoch
w i
(k-1)
B
y i
(k-1)
y i
(k)
cwnd
Throughput
t 0
(k) t 1
(k) t 2
(k)
Time (RTT)
(a) cwnd
t 0
(k) t 1
(k) t 2
(k)
Time (RTT)
(b) Throughput
Figure 5.9: Evolution of TCP congestion window cwnd and throughput w.r.t.
time.
cwnd dynamic of the i th flow at the end of the k th congestion epoch, w i (k),
can be represented as:
w i (k + 1) = βw i (k) + αT (k) (5.1)
where α and β are the increase and decrease parameters of Additive
Increase Multiplicative Decrease (AIMD) such that α = 1 and β = 0.5 (See
Section 4.3).
Let t 0 (k) be the start time of the k th congestion epoch. At time t 1 (k) the
queue begins to fill, and at a subsequent time t 2 (k) congestion occurs and a
packet is lost. For the period t 1 (k)−t 0 (k), the number of packets placed into
the network is related to the increase parameter α × T where T is the RTT
of the flow. After t 1 (k), putting extra packets into the network is simply
buffered in the bottleneck queue of size q, whilst the throughput of the flow
remains at the line rate B. At time t 2 (k) the queue overflows and congestion
is assumed to be signaled immediately, causing the TCP flow to back-off its
throughput such that the new throughput is β × P where P is the “pipe”
P = BT + q, i.e. the Bandwidth Delay Product (See Section 4.2.2) worth of