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.

拥塞窗口大小分布在TCP中很重要，因为它揭示了发送速率的统计变化。它还可以量化网络拥塞状况。使用半马尔可夫模型来开发用于解决TCP拥塞窗口大小的精确数学框架。新模型提高了文献中用于拥塞窗口大小分布的数学模型的准确性。加权指数随机变量总和的正确统计信息将被识别，并将其合并到新的数学模型中。Matlab和NS2的仿真结果证明了新模型的准确性。在一个示例中，新模型预测97.5％的拥塞窗口的长度小于82，而先前接受的模型预测97.5％的窗口的尺寸小于72，