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# Flinders Open Access Research

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### Browsing Flinders Open Access Research by Author "Abbad, Mohammed"

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Item Aggregation-disaggregation algorithm for e2-singularly perturbed limiting average Markov control problems(Institute of Electrical and Electronic Engineers, 1991) Abbad, Mohammed; Filar, Jerzy AShow more 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.Show more Item Algorithms for singularly perturbed limiting average Markov Control Problems(Institute of Electrical and Electronic Engineers, 1990) Abbad, Mohammed; Filar, Jerzy A; Bielecki, Tomasz RShow more The authors consider a singularly perturbed Markov decision process (MDP) with the limiting average cost criterion. It is assumed that the underlying process is composed of n separate irreducible processes, and that the small perturbation is such that it 'unites' these processes into a single irreducible process. This structure corresponds to the Markov chains admitting strong and weak interactions. The authors introduce the formulation and some results given by Bielecki and Filar (1989) for the underlying control problem for the singularly perturbed MDP, the limit Markov control problem (limit MCP). It is demonstrated that the limit MCP can be solved by a suitably constructed linear program. An algorithm for solving the limit MCP based on the policy improvement method is constructed.Show more Item Perturbation and stability theory for Markov control problems(Institute of Electrical and Electronic Engineers, 1992) Abbad, Mohammed; Filar, Jerzy AShow more A unified approach to the asymptotic analysis of a Markov decision process disturbed by an ε-additive perturbation is proposed. Irrespective of whether the perturbation is regular or singular, the underlying control problem that needs to be understood is the limit Markov control problem. The properties of this problem are the subject of this study.Show more Item Perturbation theory for semi-Markov control problems(Institute of Electrical and Electronic Engineers, 1991) Abbad, Mohammed; Filar, Jerzy AShow more In earlier work, the authors considered the perturbation of systems undergoing Markov processes in which the times between two consecutive decision time points were equidistant. They now consider perturbations of processes for which the times between transition are random variables. These are called semi-Markov processes.Show more