  The Transmission Control Protocol (TCP) is a Transport Protocol used in the
Internet. Ott has introduced a more general class of candidate Transport
Protocols called "protocols in the TCP Paradigm". The long run objective of
studying this larger class is to find protocols with promising performance
characteristics. This paper studies Markov chain models derived from protocols
in the TCP Paradigm. Protocols in the TCP Paradigm, as TCP, protect the network
from congestion by reducing the "Congestion Window" (the amount of data allowed
to be sent but not yet acknowledged) when there is packet loss or packet
marking, and increasing it when there is no loss. When loss of different
packets are assumed to be independent events and the probability p of loss is
assumed to be constant, the protocol gives rise to a Markov chain {W_n}, where
W_n is the size of the congestion window after the transmission of the n-th
packet. For a wide class of such Markov chains, we prove weak convergence
results, after appropriate rescaling of time and space, as p tends to 0. The
limiting processes are defined by stochastic differential equations. Depending
on certain parameter values, the stochastic differential equation can define an
Ornstein-Uhlenbeck process or can be driven by a Poisson process.
