A Storage Model with a Two-State Random Environment

Offer Kella · Ward Whitt

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Advanced Queuing Theory Analysis Reliability and Maintenance Optimization Age of Information Optimization

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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References

1987Applied Probability and Queues 1986Queueing systems with vacations ? A survey 1987Brownian Motion and Stochastic Flow Systems.1985Queues and Point Processes.1985Applications of Queueing Theory 1991Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations 1983Applications of Queueing Theory.

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