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

Authors:
G. Yin;Q. Zhang;Q. G. Liu
Affiliations:
Department of Mathematics, Wayne State University, Detroit, MI 48202, E-mail: gyin@math.wayne.edu;Department of Mathematics, University of Georgia, Athens, GA 30602, E-mail: qingz@math.uga.edu;Department of Mathematics, Wayne State University, Detroit, MI 48202, E-mail: qgliu@math.wayne.edu
Venue:
Probability in the Engineering and Informational Sciences
Year:
2000

Citing 4
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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.