Optimal scheduling control in a multi-class fluid network

A fluid network is a deterministic network model in which dynamic continuous flows are circulated among and processed at a set of stations. The model often describes the asymptotic behavior of a stochastic queuing network by the functional strong law of large numbers. The scheduling of multiple classes of fluid traffic in such a network is studied, and it is shown that the solution can be systematically derived by solving a sequence of linear programming problems. In a single-station model, the solution procedure recovers the priority index set that solves the corresponding discrete queuing model, generally known as Killimov's problem.