  This paper, based on the compactness-continuity and finite value conditions,
establishes the sufficiency of the class of stationary policies out of the
general class of history-dependent ones for a constrained continuous-time
Markov decision process in Borel state and action spaces with total nonnegative
cost criteria. The controlled process is not necessarily absorbing, the
discount factor can be identically equal to zero, and the transition rates can
also be equal to zero, which account for the major technical difficulties.
Models with these features seemingly had not been handled in the previous
literature.
