For the Borel model of the continuous-time Markov decision process, we introduce a wide class of control strategies. In a particular case, such strategies transform to the standard relaxed strategies, intensively studied in the last decade. In another special case, if one restricts to another special subclass of the general strategies, the model transforms to the semi-Markov decision process. Further, we show that the relaxed strategies are not realizable. For the constrained optimal control problem with total expected costs, we describe the sufficient class of realizable strategies, the so-called Poisson-related strategies. Finally, we show that, for solving the formulated optimal control problems, one can use all the tools developed earlier for the classical discrete-time Markov decision processes.