 
Summary: 1
TCP modeling in the presence of nonlinear window growth
Eitan Altman a , Kostia Avrachenkov a , Chadi Barakat a , Rudesindo N’u”nezQueija b
a INRIA, Sophia Antipolis, France. Email: {altman,kavratch,cbarakat}@sophia.inria.fr.
b CWI, Amsterdam, The Netherlands. Email: sindo@cwi.nl.
We develop a model for TCP that accounts for both sublinearity and limitation of
window growth. Sublinear window growth is observed when the roundtrip time of the
connection increases with the window size. Limitation is due to the window advertised by
the receiver. First, we derive the conditions for the stability of the model. Then, we write
the Kolmogorov equation under Markovian assumptions. The model is solved analytically
for some particular cases. A good match between the throughput predicted by the model
and the throughput measured on real TCP connections is reported at the end.
1. Introduction
TCP congestion control is often analyzed using linearincrease multiplicativedecrease
models for window variation [2,6,8,9,13]. These models assume that the window increases
linearly with time until a congestion occurs. At the moments of congestion, they assume
that the window decreases multiplicatively by a factor of one half. The average roundtrip
time (denoted RTT ) is used to calculate the window increase rate between congestion
events. In particular, the window increase rate is taken equal to 1/(bRTT ) packets/s,
where b is the number of packets covered by a TCP acknowledgement (ACK).
