Stochastic Models for Throughput Analysis of Randomly Arriving Elastic Flows in the Internet

This paper is about analytical models for calculating the average bandwidth shares obtained by TCP controlled finite file transfers that arrive randomly and share a single (bottleneck) link. Owing to the complex nature of the TCP congestion control algorithm, a single model does not work well for all combinations of network parameters (i.e., mean file size, link capacity, and propagation delay). We propose two models, develop their analyses, and identify the regions of their applicability. One model is obtained from a detailed analysis of TCP's AIMD adaptive window mechanism; the analysis accounts for session arrivals and departures, and finite link buffers. It is essentially a processor sharing (PS) model with time varying service rate; hence we call it TCP-PS. The other model is a simple modification of the PS model that accounts for large propagation delays; we call this model rate limited-PS (RL-PS). The TCP-PS model analysis accommodates a general file size distribution by approximating it with a mixture of exponentials. The RL-PS model can be used for general file size distributions. We show that the TCP-PS model converges to the standard PS model as the propagation delay approaches zero. We also observe that the PS model provides very poor estimates of throughput unless the propagation delay is very small. We observe that the key parameters affecting the throughput are the bandwidth delay product (BDP), file size distribution, the link buffer and the traffic intensity. Several numerical comparisons between analytical and simulation results are provided. We observe that the TCP-PS model is accurate when the BDP is small compared to the mean file size, and the RL-PS model works well when the BDP is large compared to the mean file size