# TCP Network Calculus: The case of

##
Konstantin E. Avrachenkov

### INRIA Sophia Antipolis

### Résumé:

We present an analytical model for the
calculation of network load and drop probabilities
in a TCP/IP network with general topology. First we
formulate our model as a nonlinear complementarity problem.
Then we transform the model into two equivalent formulations:
fixed point formulation and nonlinear programming formulation.
These equivalent formulations provide efficient computational
procedures for the solution of our model. Furthermore, with
the help of the fixed point formulation we are able to prove
the existence of a solution. Our model has the main advantage
of not requiring the pre-definition of bottleneck links.
The model also takes into account the receiver congestion
window limitation. Our approach can be used for TCP/IP networks
with drop tail routers as well as for TCP/IP networks with
active queue management routers. We solve the problem for
some network examples and we show how the distribution of load
varies with network parameters. The distribution of load is
sometimes counter-intuitive which cannot be detected by other
models making prior assumptions on the locations of bottlenecks.

This is a joint work with E. Altman and C. Barakat.