A fluid network is a deteministic network model in which dynamic continious flows are circulated and processed among a set of stations. A fluid network often describes the asymptotic behavior of a stochastic queueing network via functional strong law of large numbers. The dynamic scheduling of multiple classes of fluid traffic in such a network was studied. An algorithm is developed that systematically solves the dynamic scheduling problem by solving a sequence of linear programs. It generates a policy, in the form of dynamic capacity allocation at each station that consists of a finite set of linear `pieces' over the entire time horizon. In a single-station, or equivalently, single-server network, this solution procedure recovers the priority index set that is optimal for the corresponding discrete queueing model, generally known as Klimov`s problem.
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