Optimal control of single-server fluid networks

We consider a stochastic single-server fluid network with both a discounted reward and a cost structure. It can be shown that the optimal policy is a priority index policy. The indices coincide with the optimal indices in a semi-Markovian Klimov problem. Several special cases like single-server reentrant fluid lines are considered. The approach we use is based on sample path arguments and Pontryagin's maximum principle.