A Multilevel Approach for the Modelling of Large TCP/IP Networks

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. Our model does not require the predefinition of bottleneck links. The model is based on analytical expressions for TCP throughput, which allows it to take into account diverse TCP features as the receiver congestion window limitation. It can be used for TCP/IP networks with drop tail routers as well as for TCP/IP networks with active queue management routers. First, we formulate our model as a Non- Linear Complementarity problem (NCP). Then, we transform the model into two equivalent formulations: fixed point formulation and nonlinear programming formulation. Thereupon, using asymptotic analysis, we prove existence of a unique solution to the NCP by casting it into the well known utility optimization framework. In addition to uniqueness of rates and end-to-end drop probabilities, the NCP shows the ability to provide unique solutions in terms of link drop probabilities. We explain the relationship between the utility optimization, fixed-point approach and our complementarity approach. Specifically, we show how these models can be derived from each other. Finally, we illustrate the utility of our proposed approach by solving some benchmark examples and showing 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.