We consider the performance of a network like the Internet handling so-call
ed elastic traffic where the rate of flows adjusts to fill available bandwi
dth. Realized throughput depends both on the way bandwidth is shared and on
the random nature of traffic. We assume traffic consists of point to point
transfers of individual documents of finite size arriving according to a P
oisson process. Notable results are that weighted sharing has limited impac
t on perceived quality of service and that discrimination in favour of shor
t documents leads to considerably better performance than fair sharing. In
a linear network, max-min fairness is preferable to proportional fairness u
nder random traffic while the converse is true under the assumption of a st
atic configuration of persistent flows. Admission control is advocated as a
necessary means to maintain goodput in case of traffic overload.