On the dynamics and performance of stochastic fluid systems

On the dynamics and performance of stochastic fluid systems

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Article ID: iaor2004786
Country: United States
Volume: 37
Issue: 3
Start Page Number: 652
End Page Number: 667
Publication Date: Sep 2000
Journal: Journal of Applied Probability
Authors: ,
Keywords: stochastic processes
Abstract:

A (generalized) stochastic fluid system Q is defined as the one-dimensional Skorokhod reflection of a finite variation process X (with possibly discontinuous paths). We write X as the (not necessarily minimal) difference of two positive measures, A, B, and prove an alternative ‘integral representation’ for Q. This representation forms the basis for deriving a ‘Little's law’ for an appropriately constructed stationary version of Q. For the special case where B is the Legesgue measure, a distributional version of Little's law is derived. This is done both at the arrival and departure points of the system. The latter result necessitates the consideration of a ‘dual process’ to Q. Examples of models for X, including finite variation Lévy processes with countably many jumps on finite intervals, are given in order to illustrate the ideas and point out potential applications in performance evaluation.

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