Fluid approximation of a controlled multiclass tandem network

A two-station, four-class queueing network with dynamic scheduling of serve rs is analyzed. It is shown that the corresponding Markov decision problem converges under fluid scaling to a fluid optimal control model. The structu re of the optimal policy for the fluid network, and of an asymptotically op timal policy for the queueing network are derived in an explicit form. They concur with the tandem mu-rule, if this policy gives priority to the same flow of customers in both stations. In general, they are monotone with a li near switching surface.