**A closed form formula for TCP traffic performance:
Homogeneous long-lived flows**

**A. Chaintreau and De Vleeschauwer**

**Abstract:**

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 user 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.