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Stability and Structural Properties of Stochastic Storage Networks

Kella, Offer; Whitt, Ward

We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multi-dimensional content process is tight under the natural stability condition. The multi-dimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content process is monotone in its initial conditions. Hence, when any content process with nonzero initial conditions hits the origin, it couples with the content process starting at the origin. However, in general, a tight content process need not hit the origin.

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Title
Journal of Applied Probability
DOI
https://doi.org/10.2307/3214994

More About This Work

Academic Units
Industrial Engineering and Operations Research
Published Here
September 19, 2017
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