  We consider a stochastic model of Internet congestion control, introduced by
Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that
represents the randomly varying number of flows in a network where bandwidth is
shared among document transfers. In contrast to an earlier work by Kelly and
Williams [Ann. Appl. Probab. 14 (2004) 1055--1083], the present paper allows
interarrival times and document sizes to be generally distributed, rather than
exponentially distributed. Furthermore, we allow a fairly general class of
bandwidth sharing policies that includes the weighted $\alpha$-fair policies of
Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567], as well
as certain other utility based scheduling policies. To describe the evolution
of the system, measure valued processes are used to keep track of the residual
document sizes of all flows through the network. We propose a fluid model (or
formal functional law of large numbers approximation) associated with the
stochastic flow level model. Under mild conditions, we show that the
appropriately rescaled measure valued processes corresponding to a sequence of
such models (with fixed network structure) are tight, and that any weak limit
point of the sequence is almost surely a fluid model solution. For the special
case of weighted $\alpha$-fair policies, we also characterize the invariant
states of the fluid model.
