Convex Stochastic Fluid Programs with Average Cost

We consider stochastic fluid programs under the average cost criterion.These models have been introduced by the author (in press, Math. Oper. Res.) and are of the following type: suppose Zt is a continuous-time Markov chain with finite state space.As long as Zt = z, the dynamics of the system at time t are given by a linear function bz a · , where a is a control we have to choose.A convex cost rate function c is given, depending on the state and the action.W e want to control the system in such a way as to minimize the expected average cost.Such models typically appear in production and telecommunication systems.Using a vanishing discount approach and a discretization technique, we show that the relative value function satisfies a HJB equation and derive a verification theorem.L ast but not least we apply our results to manufacturing systems and network problems