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Ergodicity of age-dependent inventory control systems. (English) Zbl 1351.60115

Summary: We consider continuous review inventory systems with general doubly stochastic Poisson demand. In this specific case the demand rate, experienced by the system, varies as a function of the age of the oldest unit in the system. It is known that the stationary distributions of the ages in such models often have a strikingly simple form. In particular, they exhibit a typical feature of a Poisson process: given the age of the oldest unit the remaining ages are uniform. The model we treat here generalizes some known inventory models dealing with partial backorders, perishable items, and emergency replenishment. We derive the limiting joint density of the ages of the units in the system by solving partial differential equations. We also answer the question of the uniqueness of the stationary distributions which was not addressed in the related literature.

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K25 Queueing theory (aspects of probability theory)
90B05 Inventory, storage, reservoirs
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