Abstract: Markov decision process can model complex system with nondeterminism．Schedulers are required to resolve the nonderministic choices during model analysis．This paper introduced the time-and space-bounded reachability probabilities of markov decision process under different schedulers．Firstly,the formal definition and classification method of schedulers for nonderminism were proposed and then we proved that the reachability probabilities coincide for determini-stic and randomized schedulers under time-abstract．Also,it was proved that time-dependent scheduler generally induces probability bounds that exceed those of the corresponding time-abstract．At the end of paper,two cases were illustrated for describing the correctness of the conclusion.

Key words: Markov decision process,Nonderministic scheduler,Time-and space-bounded reachability probability