  The present report deals with the modeling of the long-term throughput,
a.k.a., send rate, of the Transmission Control Protocol (TCP) under the
following assumptions. (i) We consider a single 'infinite source' using a
network path from sender to receiver. (ii) Each TCP packet is randomly dropped
with probability p; independently of previous drops or any other
event/parameter. (iii) The - never changing - receiver window limits the amount
of outstanding data. (iv) The receiver acknowledges every packet. (v) The TCP
modeled here conforms to the publicly available standards (RFCs) as concerns
congestion control. We validate and determine the limits of the different
models proposed here using packet-level simulations. The contributions of the
present work are the following: (a) We determine three regimes, and their
conditions of applicability, depending on p: Linear law regime, square root law
regime, and timeout regime. (b) As concerns the relationship between the linear
and square root regimes, we give additional insights relatively to previously
published work. (c) We give the exact equations governing the TCP send rate in
any regime. (d) From the exact equation and under the further condition that
the path is not saturated, we give and discuss approximations for the send rate
of the NewReno variant of TCP. A by-product of these calculations is the
distribution of the sender window, independently of any timing or saturation
consideration. (e) These approximations give results that are accurate to a few
percent when compared to simulation results. Detailed comparison and sources of
errors between theory and simulations are also discussed.
