This paper explores a natural generalization of the classic tandem-queue model, designed specifically to represent make- to-stock production processes. In such systems, intermediate and finished goods can be produced and stored in advance of demand. We consider the simplest version of the model, where demand is a Poisson process, and the unit production times are exponentially distributed. We propose and test a tractable approximation scheme. The approximation appears to be quite accurate.
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Lee et al. (1992) studied this question.