This paper is devoted to the approximate solution of a strongly NP-hard resource-constrained scheduling problem which arises in relation to the operability of certain high availability real time distributed systems. We present an algorithm based on the simulated annealing metaheuristic and, building on previous research on exact solution methods, extensive computational results demonstrating its practical ability to produce acceptable solutions, in a precisely defined sense. Additionally, our experiments are in remarkable agreement with certain theoretical properties of our simulated annealing scheme. The paper concludes with a short discussion on further research.