Stability of real-time lot-scheduling and machine replacement policies with quality levels

We consider a single machine, multiproduct manufacturing system which can operate at finitely many quality levels. The quality of the machine deteriorates according to a continuous-time Markov process and the only way to improve the quality is by replacing the machine by a new one. In this framework we derive conditions for the stability of the system under a simple class of real-time scheduling/replacement policies. The stability notion that we employ is the recurrence of the total work backlog.