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We consider a stochastic model of Internet congestion control, introduced byMassouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], thatrepresents the randomly varying number of flows in a network where bandwidth isshared among document transfers. In contrast to an earlier work by Kelly andWilliams [Ann. Appl. Probab. 14 (2004) 1055--1083], the present paper allowsinterarrival times and document sizes to be generally distributed, rather thanexponentially distributed. Furthermore, we allow a fairly general class ofbandwidth sharing policies that includes the weighted $\alpha$-fair policies ofMo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567], as wellas certain other utility based scheduling policies. To describe the evolutionof the system, measure valued processes are used to keep track of the residualdocument sizes of all flows through the network. We propose a fluid model (orformal functional law of large numbers approximation) associated with thestochastic flow level model. Under mild conditions, we show that theappropriately rescaled measure valued processes corresponding to a sequence ofsuch models (with fixed network structure) are tight, and that any weak limitpoint of the sequence is almost surely a fluid model solution. For the specialcase of weighted $\alpha$-fair policies, we also characterize the invariantstates of the fluid model.

Fluid limits for networks with bandwidth sharing and general document size distributions