An application to the finite approximation of the first passage models for discrete-time Markov decision processes with varying discount factors

This paper deals with the approximation problem of the first passage models for discrete-time Markov decision processes (MDPs) with varying discount factors. For a given control model M, by using a finite-state and finite-action truncation technique, we show that the first passage optimal reward and policies of M can be approximated by those of the solvable truncated control models, and illustrate the finite approximation by a controlled queueing system in numerical results.