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.
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