Dynamic scheduling of a multiclass fluid network

A fluid network is a deterministic network model in which dynamic continuous 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. We study the dynamic scheduling of multiple classes of fluid traffic in such a network. 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 (among all fluids classes), 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.