A Storage Model with a Two-State Random Environment

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Abstract
Motivated by queues with service interruptions, we consider an infinite-capacity storage model with a two-state random environment. The environment alternates between “up” and “down” states. In the down state, the content increases according to one stochastic process; in the up state, the content decreases according to another stochastic process. We describe the steady-state behavior of this system under assumptions on the component stochastic elements. For the special case of deterministic linear flow during the up and down states, we show that the steady-state content is directly related to the steady-state workload or virtual waiting time in an associated G/G/1 queue, thus supplementing the results of D. P. Gaver, Jr., and R. G. Miller, Jr. (1962), R. G. Miller, Jr. (1963) and H. Chen and D. D. Yao (1992).

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