In this paper we study an ``idealized'' version of TCP/IP. Unlike in for example TCP Reno, loss of two or more packets within one Congestion Window (or within one Round Trip Time) does not lead to collapse and time-out. As such, the results are a prediction of the performance of TCP if (for example by using Selective Acknowledgements) it is made perfectly robust under packet corruption or packet loss, but still follows the basic TCP ideas on how to grow the congestion window during congestion avoidance, and how to decrease (halve) the window at detection of packet loss or corruption. The model we use can also serve to study the performance of TCP under other proposed modifications.
In this idealized TCP/IP, if for successive packets loss is independent, the congestion window sizes after successive packets becomes markov process. If the probability of loss is constant, that markov process has a stationary distribution. In this paper we study that stationary distribution, in the situation of (moderate to very) low loss probability and an adverised window large enough not to affect the evolution of the congestion window.
For a fluid flow approximation to that process we obtain the stationary distribution and all its moments. The shape of the stationary distribution indicates that the packet loss probability does not need to be very low for the approximation to be valid.
The results have already proven useful in understanding, among others, simulation results of TCP over ATM with ABR or UBR.