Inventory system for goods with censored random lifetimes

We consider a Poisson inventory model for perishable goods in which the items have random lifetimes and are scrapped either when reaching the end of their lifetime or a fixed constant expiration age. The crucial process to describe this system is the virtual death process (W(t)) (defined for t ⩾ 0), where W(t) is the residual waiting time after time t until the next ‘death’ of an item if there were no demand arrivals after t. We derive its stationary law in closed form and determine the distribution of the number of items in the system (also in steady state).