A closed form formula for long-lived TCP connections throughput

In this paper, we study the variation of the throughput achieved by TCP resulting from both the individual behavior of a connection and the interaction with all other connections sharing the same link. In particular, we calculate the tail distribution function (TDF) of the instantaneous throughput seen by one TCP connection in the additive increase multiplicative decrease (AIMD) framework. For the particular case that each TCP connection experiences the same round trip time (RTT) and under the many users approximation we prove that this TDF is given by a closed form formula that solely depends on the network parameters (number of sources, capacity and buffer size of the bottleneck link). This formula can then be used as a dimensioning tool, where throughput is guaranteed to each user to be “larger than a given value for at least a certain percentage of the time”. In the context defined here, this formula plays the same role for the dimensioning of an IP router as the Erlang B formula does for the dimensioning of a PSTN switch.