Abstract
This Paper investigates the model of a continuous time Markov decision decision Process (CTMDP for short) in a semi Markov environment with discounted criterion. The model describe a system Which behaves like a CTMDP except that the system is influenced by its environment Which is described by a semi-Markov Process Following each change of the environment states there occur three things:1) an instantancous state (of the system ) transition:2) an instantaneous reward:3) the Paramenters of the CTMDP varify. After presenting the precise formulation of the model, we prove the optimality equation and the existence of ∊,-optimal policies. then approximating results are obtained when the underlying distribution functions (d.f.s) of the semi-Markov environment are approximated, and the special case of phase type environment is treated.
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