Double band policy for a failure prone manufacturing system with alternate demand rates in heavy traffic

We consider a manufacturing system with a single failure prone machine producing a single part type whose demand changes randomly and alternately between constant rates the successive periods of which are represented by i.i.d. random variables, as are the successive up and down periods of the machine state. We assume that the additional products can be bought with a zero lead time, and that the system operates in heavy traffic. The control objective is to minimise the expected discounted total cost. An asymptotically optimal policy is obtained using a diffusion approximation scheme.