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In the first part of this talk, we present a simple ordinary differential equation model of data flow through nodes in a computer processor network. Under an appropriate asymptotic scaling, this model approximates a partial differential equation which treats data as a continuum fluid and takes the form of a non-standard conservation law. From this conservation law, we derive a Hamilton-Jacobi equation for which the existence and uniqueness of solutions can be proven. We then present numerical results that demonstrate qualitative agreement between the discrete and continuum models, and we explore the effects of variations in the parameters of the computing environment. In the second part of the talk, we introduce an auxiliary variable, reformulate the continuum model as a PDE system, and define weak solutions. We then identify a special class of solutions which take the form of piecewise constants separated by fronts. Qualitative properties such as propagation speed and stalling are investigated, both theoretically and numerically.