The Weak Convergence of TCP Bandwidth Sharing
  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. 
Wolfram Lautenschlaeger
cs.NI