MODELLING AND STABILITY OF FAST TCP

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1. Introduction. Congestion control is a distributed feedback algorithm
to allocate network resources among competing users. The algorithms
in the current Internet, TCP Reno, have prevented severe congestion
while the Internet underwent explosive growth during the last decade. It is
well known however that TCP Reno's performance degrades steadily as networks
continue to scale up in capacity and size [5, 12]. This has motivated
several recent proposals for congestion control of high-speed networks, including
HSTCP [4], Scalable TCP [10], FAST TCP [7, 8], and BIC TCP
[19] (see [7, 8] for extensive references). The details of the architecture,
algorithms, experimental evaluations of FAST TCP can be found in [7, 8].
A new discrete-time model of congestion control is also introduced in [7, 8]
and a sucient condition for the local asymptotic stability of FAST TCP
is proved using the new model for the case of a single page link in the absence
of feedback delay. In this paper, we extend the analysis and prove four
stability results.


JIANTAO WANG ET AL.
In reality, a source dynamically sets its congestion window rather than
its sending rate. These models do not adequately capture the self-clocking
eect where a packet is sent only when an old one is acknowledged, except
brie
y and immediately after the congestion window is changed. This automatically
constrains the input rate at a page link to its page link capacity, after a
brief transient, no matter how large the congestion windows are set. The
new discrete-time page link model proposed in [7, 8] captures this eect. While
the traditional continuous-time page link model does not consider self-clocking,
the new discrete-time page link model ignores the fast dynamics at the links. We
present both models of FAST TCP in Section 2. Experimental results are
provided to show that, despite errors in these models, both of them seem
to track the queue process reasonably well. Then we prove two stability
results in each of these models.
In Section 3, we prove that FAST TCP is globally asymptotically
stable in general networks when there is no feedback delay using the
continuous-time model. We also derive a sucient condition for local
asymptotic stability in general networks with feedback delay, using the
techniques developed in [13, 16].

2.1. Notation. A network consists of a set of L links indexed by l
with nite capacity cl. It is shared by a set of N
ows identied by their
sources indexed by i. Let R be the routing matrix where Rli = 1 if source
i uses page link l, and 0 otherwise.
We use t for time in the continuous-time model, and for time step in
the discrete-time model. The meaning of t should be clear from the context.
FAST TCP updates its congestion window every xed time period, which
is used as the time unit.