Convex Stochastic Fluid Programs with Average Cost

✍ Scribed by Nicole Bäuerle

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 160 KB
• Volume: 259
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7400

✦ Synopsis

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 Z t is a continuous-time Markov chain with finite state space. As long as Z t = z, the dynamics of the system at time t are given by a linear function b z 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. We 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. Last but not least we apply our results to manufacturing systems and network problems.