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- TCP Analysis
- Full Paper
- TCP is Max-Plus Linear
Francois Baccelli (ENS-INRIA)
Dohy Hong (ENS-INRIA)
We give an exact representation of the packet-level dynamical behavior
of the Reno and Tahoe variants of TCP over a single end-to-end connection.
This representation allows one to consider the case when the
connection involves a network made of several, possibly heterogeneous,
deterministic or random routers in series.
It is shown that all key features of the protocol and of the network
can be expressed via a linear dynamical system in the so called
max-plus algebra. This opens new ways of both analytical evaluation and fast
simulation based on products of matrices in this algebra.
This also leads to closed form formulas for the throughput
allowed by TCP and for the detailed dynamical
behavior of the routers; these new formulas are shown to
refine those obtained from earlier models which either assume that the network
could be reduced to a single bottleneck router and/or approximate
the packets by a fluid.