caa a22 4500 44583109X CHVBK 20180317145315.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10255-011-0061-2 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0061-2 First passage models for denumerable semi-Markov decision processes with nonnegative discounted costs [Elektronische Daten] [Yong-hui Huang, Guo Xian-ping] This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal (or ɛ-optimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach. Further we give some properties of optimal policies. In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 Semi-Markov decision processes nationallicence target set nationallicence first passage time nationallicence discounted cost nationallicence optimal policy nationallicence Huang Yong-hui School of Mathematics and Computational Science, Sun Yat-Sen University, 510275, Guangzhou, China aut Xian-ping Guo School of Mathematics and Computational Science, Sun Yat-Sen University, 510275, Guangzhou, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/2(2011-04-01), 177-190 0168-9673 27:2<177 2011 27 10255 https://doi.org/10.1007/s10255-011-0061-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0061-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Huang Yong-hui School of Mathematics and Computational Science, Sun Yat-Sen University, 510275, Guangzhou, China aut NATIONALLICENCE 700 1- Xian-ping Guo School of Mathematics and Computational Science, Sun Yat-Sen University, 510275, Guangzhou, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/2(2011-04-01), 177-190 0168-9673 27:2<177 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer