  TCP is the dominating transmission protocol in the Internet since decades. It
proved its flexibility to adapt to unknown and changing network conditions. A
distinguished TCP feature is the comparably fair resource sharing.
Unfortunately, this abstract fairness is frequently misinterpreted as
convergence towards equal sharing rates. In this paper we show in theory as
well as in experiment that TCP rate convergence does not exist. Instead, the
individual TCP flow rate is persistently fluctuating over a range close to one
order of magnitude. The fluctuations are not short term but correlated over
long intervals, so that the carried data volume converges rather slowly. The
weak convergence does not negate fairness in general. Nevertheless, a
particular transmission operation could deviate considerably.
