Accurate mathematical modeling and solution of TCP congestion window size distribution

Abstract

The congestion window size distribution is important in TCP as it reveals the statistical variation of the sending rate. It also quantifies the network congestion conditions. A semi-Markov model is used to develop an accurate mathematical framework for solving for TCP congestion window size. The new model improves on the accuracy of a widely accepted mathematical model in the literature for the congestion window size distribution. The correct statistics of a sum of weighted exponential random variables are identified and incorporated into the new mathematical model. Simulation results from both Matlab and NS2 demonstrate the accuracy of the new model. In one example, the new model predicts that 97.5% of congestion windows will have length less than 82 whereas the previous accepted model predicts 97.5% of the windows will have sizes less than 72, and hence the previous model can lead to buffer and caching requirement estimates that are too small when designing practical networks.