  In this paper, we consider multi-dimensional maximal cost-bounded
reachability probability over continuous-time Markov decision processes
(CTMDPs). Our major contributions are as follows. Firstly, we derive an
integral characterization which states that the maximal cost-bounded
reachability probability function is the least fixed point of a system of
integral equations. Secondly, we prove that the maximal cost-bounded
reachability probability can be attained by a measurable deterministic
cost-positional scheduler. Thirdly, we provide a numerical approximation
algorithm for maximal cost-bounded reachability probability. We present these
results under the setting of both early and late schedulers.
