Optimal control of systems with random influences: Operations Research models
Stochastic models of Operations Research –––>
This is a joint project with Pavel S. Knopov (V. M. Glushkov Institute of Cybernetics, Academy of Science of the Ukraina). The project is funded by the DFG (Germany).
(1) We consider stochastic models from the field of Operations Research (queueing systems, inventory sytems, repair and renewal sytems) subject to an external (open loop) control by a decision maker. The aim is to find simple optimal or nearly optimal control policies which minimize the long range costs (maximize the long range reward). The common feature of the models is the contiuous state space of the describing system processes; so the variable (observation) where the control decision is based on is continuous.
(2) Stochastic networks are random fields on graphs, when considered at a fixed time instant. Incoprorating the space–time variabilty of such systems leads to time dependent random fields. If the systems are controlled by decision makers which act at the nodes and make their decisions on the basis of local information only, and if the space–time behavior of the system carries Markov structures in time and space, we obtain controlled Markov processes with locally interacting components. Our interest is in finding optimal strategies inside the class of local strategies and in proving conditions which guarantee that these locally optimal strategies are even globally optimal.
Collaboration with Ludmila P. Tur (Kiew) and Ruslan K. Chornei (Kiew).
Some recent articles concerning Optimal control of systems with random influences: Operations Research models :
- Optimal admission control for M/D/1/K queueing systems (with Pavel S. Knopov )
Mathematical Methods of Operations Research 50 (1999), p. 91–100 - Optimal strategies for an inventory systems with cost functions of general form (with Pavel S. Knopov and Ludmila P. Tur )
Cybernetics and System Analysis 35, 602 – 618, 1999
(Translation from Kibernetica i Sistemyi Analiz 4' 99, 106–123, 1999) - Local control of interacting Markov fields on graphs with compact state space (with Ruslan K. Chornei and Pavel S. Knopov)
Kibernetica i Sistemyi Analiz 2001, No. 3 p. 62 – 77, also available as
Preprint No.2000–09, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2002. - Stochastic games for distributed players on graphs (with Ruslan K. Chornei and Pavel S. Knopov)
Mathematical Methods of Operations Research 60, 279–298, 2004
Preliminary version: Preprint No.2002–06, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2002. - Controlled semi-Markov fields with graph-structured compact state space (with Ruslan K. Chornei and Pavel S. Knopov)
Theory of Probability and Mathematical Statistics 69, 39–53, 2004
translation from: Teor. Ymovirnost. Matem. Statist. 69, 42–47, 2003, (in Ukrainian)
also available as Preprint No.2002–08, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2002. - Controlled Markov fields with finite state space on graphs ( with Ruslan K. Chornei and Pavel S. Knopov)
Stochastic Models 21, 847–874, 2005
also available: Preprint No.2000–08, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2000. - Control of Spatially Structured Random Processes and Random fields with Applications ( with Ruslan K. Chornei and Pavel S. Knopov) Springer, New York, 2006