Summary
This paper aims to give a non-technical introduction to the field of stochastic control, particularly to Markov decision control. The emphasis is on the basic concepts of the Markov decision model and on giving an idea of the practical usefulness of this model in a variety of application areas. Also, the value-iteration algorithm with lower and upper bounds on the average costs will be discussed; this method is easy to apply in practice and is usually the most effective method for solving large-scale Markov decision problems.
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A. Federgruen, H. Groenevelt and H.C. Tijms (1984), Coordinated replenishments in a multi-item inventory system with compound Poisson demands, Manag. Sci., 30, 344–357.
F. Kamoun and L. Kleinrock (1980), Analysis of a shared finite storage in a computer network node environment under general traffic conditions, IEEE Trans. Commun., 28, 992–1003.
B.S. Maglaris and M. Schwartz (1982), Optimal fixed frame multiplexing in integrated line-and packet-switched communication networks, IEEE Trans. Inform. Th., 28, 263–273.
P. Nain and K.W. Ross (1985), Optimal multiplexing of heterogeneous traffic with hard constraint, INRIA Report, Valbonne, France.
J.L. Popyack, R.L. Brown and C.C. White III (1979), Discrete versions of an algorithm due to Varaiya, IEEE Trans. Autom. Contr., 24, 503–504.
K.W. Ross (1985), Constrained Markov Decision Processes with Queueing Applications, Ph.D. Dissertation, CICE Program, University of Michigan.
P.J. Schweitzer (1971), Iterative solution of the functional equations of undiscounted Markov renewal programming, J. Math. Anal. Appl., 34, 495–501.
S.Y. Su and R.A. Deininger (1974), Modeling the regulation of Lake Superior under uncertainty of future water supplies, Water Resources, 10, 11–25,
H.C. Tijms, Stochastic Modelling and Analysis: A Computational Approach (1986), Wiley, Chichester.
H.C. Tijms and A.M. Eikeboom (1986), A simple technique in Markovian control with applications to resource allocation in communication networks, OR Letters, 5, 11–19.
J. Van der Wal and P.J. Schweitzer (1987), Iterative bounds on the equilibrium distribution of a finite Markov chain, Probability in the Engineering and Informational Sciences, 1.
R.C. Vergin and M. Scriabin (1977), Maintenance scheduling for multicomponent equipment, AIIE Trans. 15, 297–305.
D.J. White (1985), Real applications of Markov decision problems, Interfaces, 15, no.6, 73–83.
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© 1987 Springer-Verlag Berlin Heidelberg
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Tijms, H. (1987). Stochastic Markovian Control: Applications and Algorithms. In: Isermann, H., Merle, G., Rieder, U., Schmidt, R., Streitferdt, L. (eds) DGOR. Operations Research Proceedings 1986, vol 1986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72557-9_3
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DOI: https://doi.org/10.1007/978-3-642-72557-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17612-1
Online ISBN: 978-3-642-72557-9
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