Question: Consider a single-product inventory system in which customers asking for the product arrive according to a Poisson process with rate 1. Each customer asks for

Consider a single-product inventory system in

Consider a single-product inventory system in which customers asking for the product arrive according to a Poisson process with rate 1. Each customer asks for one unit of the product. Each demand which cannot be satisfied directly from stock on hand is lost. Opportunities to replenish the inventory occur according to a Poisson process with rate f. This process is assumed to be independent of the demand process. For technical reasons a replenishment can only be made when the inventory is zero. The inventory on hand is raised to the level 10 each time a replenishment is done. (a) What is the long-run fraction of time the system is out of stock? (b) What is the long-run fraction of demand that is lost

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