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A New Look at Urban Water Storage in a Series of Connected Dams

Part of: Basic linear algebra Markov processes Special matrices

Published online by Cambridge University Press:  30 January 2018

Phil Howlett ,
Charles Pearce  and
Julia Piantadosi
Phil Howlett*
Affiliation:
University of South Australia
Charles Pearce*
Affiliation:
University of Adelaide
Julia Piantadosi*
Affiliation:
University of South Australia
*
∗ Postal address: Scheduling and Control Group, Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes, 5095, Australia.
∗∗ Postal address: School of Mathematical Sciences, University of Adelaide, Adelaide, 5000, Australia.
∗ Postal address: Scheduling and Control Group, Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes, 5095, Australia.
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Abstract

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We propose a discrete state-space model for storage of urban stormwater in two connected dams using an optimal pump-to-fill policy to transfer water from the capture dam to the holding dam. We assume stochastic supply to the capture dam and independent stochastic demand from the holding dam. We find new analytic formulae to calculate steady-state probabilities for the contents of each dam and thereby enable operators to better understand system behaviour. We illustrate our methods by considering some particular examples and discuss extension of our analysis to a series of three connected dams.

Keywords

Urban stormwaterwater storagewater distributionsystems of connected damsMarkov decision processes

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors 15B51: Stochastic matrices 60J22: Computational methods in Markov chains
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 118 - 135
Copyright
© Applied Probability Trust 

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