We present in this paper 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.
Based on the paper:
E. Altman, K.E. Avrachenkov and C. Barakat,
"TCP network calculus: The case of large delay-bandwidth product",
IEEE INFOCOM 2002.