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On the behaviour of a long cascade of linear reservoirs

Part of: Special processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

John E. Glynn  and
Peter W. Glynn
John E. Glynn*
Affiliation:
Geological Survey of Canada
Peter W. Glynn*
Affiliation:
Stanford University
*
∗Postal address: Earth Sciences Sector, 601 Booth St., Ottawa, Ontario, K1A 0E8, Canada
∗∗Postal address: Department of Engineering-Economic Systems and Operations Research, Stanford University, Stanford, CA 94305-4023, USA
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Abstract

This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.

Keywords

Storage theorylinear cascadelarge deviationsstrong approximationcentral limit theorem

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60F05: Central limit and other weak theorems 60F10: Large deviations
Secondary: 60F15: Strong theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 417 - 428
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

This research was supported by the US Army Research Office under contract no. DAAG55-97-1-0377 and by the National Science Foundation under grant no. DMS-9704732.

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