stochastic networks are used as models for complex processing systems involving dynamic interactions subject to uncertainty. applications arise in high-tech manufacturing, the service industry, telecommunications, computer systems and bioengineering. the control and analysis of such networks present challenging mathematical problems. in this talk, a concrete application will be used to illustrate a general approach to the study of stochastic processing networks based on deriving more tractable approximate models. specifically, we will consider a model of internet congestion control in which processing can involve the simultaneous use of several resources (or links), a phenomenon that is not well understood. elegant fluid and diffusion approximations will be derived and used to study the performance of this model. a key insight from this analysis is a geometric representation of the consequences of using a "fair" policy for the sharing of resources. the talk will conclude with a summary of the current status and description of open problems associated with approximate models for general stochastic processing networks.