The (optimal) design of many engineering systems can be adequately recast as a Markov decision process, where requirements on system performance are captured in the form of constraints. In this paper, various optimality results for constrained Markov decision processes are briefly reviewed; the corresponding implementation issues are discussed and shown to lead to several problems of parameter estimation. Simple situations where such constrained problems naturally arise, are presented in the context of queueing systems, in order to illustrate various points of the theory. In each case, the structure of the optimal policy is exhibited.