## Aggregation-disaggregation algorithm for e2-singularly perturbed limiting average Markov control problems

##### Abstract

In this paper we consider a singular perturbation of order 2 for
a Markov decision process with the limiting average reward criterion.
We define a singular perturbation of order 2 in the following
sense: we assume that the underlying process is composed of n
separate irreducible processes, and that a small e-perturbation is
such that it ”unites” these processes into m separate irreducible
processes. Then another small e2-perturbation is such that it
“unites” these latter processes into a single irreducible process.
The present paper is organized as follows:
In Section 2, we formulate the singular perturbation of order 2.
In Section 3, we give explicitly the limit Markov Control
Problem (limit MCP), that is entirely different from the original
unperturbed MDP, which forms an appropriate asymptotic approximation
to a whole family of perturbed problems. Thus
only the single limit MCP needs to be solved.