An inventory system uses continuous control as follows. Demands arrive one at a time according to a PP(λ) (that means time between demands ∼ exp(λ)). When a demand arrives, if there are items in inventory, it is immediately satisfied, otherwise the demand is lost. As soon as the inventory level drops to R, an order is placed for K items from a supplier. However, the order is fulfilled after an exp(θ) amount of time. Assume that K > R. Let X(t) be the number of items in inventory at time t. Model {X(t), t ≥ 0} as a CTMC with the assumption that R < X(0) ≤ K + R.

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