Modeling and calculation of multi-bottleneck networks with large number of TCP flows

In this paper, we propose a mathematical model for calculating the steady state performance of congested networks with large number of TCP flows. Marking probability, average queue length, bandwidth and RTT are connected by a group of nonlinear equations. We transform these equations into a constrained optimization problem, which is then solved by SQP algorithm, a robust method for the optimization with inequality constraints. Numerical results with Matlab and simulation results with NS-2 are given to validate the accuracy of the model and algorithm. We study the relationship between the calculation time and congestion network parameters, and provide a good estimation of calculation time at different network scale. It is helpful for network pricing system.