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ERROR BOUNDS FOR OCCUPATION MEASURE OF SINGULARLY PERTURBED MARKOV CHAINS INCLUDING TRANSIENT STATES

Published online by Cambridge University Press:  31 October 2000

G. Yin ,
Q. Zhang  and
Q. G. Liu
G. Yin
Affiliation:
Department of Mathematics, Wayne State University, Detroit, MI 48202, E-mail: [email protected]
Q. Zhang
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, E-mail: [email protected]
Q. G. Liu
Affiliation:
Department of Mathematics, Wayne State University, Detroit, MI 48202, E-mail: [email protected]
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Abstract

Motivated by many applications in production planning, system reliability, queueing networks, and wireless communication, this work is devoted to singularly perturbed Markov chains with finite states. Focusing on nonstationary processes with the inclusion of transient states, asymptotic error bounds of a sequence of suitably scaled occupation measures are derived. The main tools used include martingales and differential equations. The results are useful for analyzing structural properties of the underlying Markov chains and for designing nearly optimal and hierarchical controls of large-scale and complex systems.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 14 , Issue 4 , October 2000 , pp. 511 - 531
Copyright
© 2000 Cambridge University Press

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