Journal of Applied Probability

A new look at urban water storage in a series of connected dams

Phil Howlett, Charles Pearce, and Julia Piantadosi

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51, Number 1 (2014), 118-135.

Dates
First available in Project Euclid: 25 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1395771418

Digital Object Identifier
doi:10.1239/jap/1395771418

Mathematical Reviews number (MathSciNet)
MR3189446

Zentralblatt MATH identifier
1297.90012

Subjects
Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors 15B51: Stochastic matrices 60J22: Computational methods in Markov chains [See also 65C40]

Keywords
Urban stormwater water storage water distribution systems of connected dams Markov decision processes

Citation

Howlett, Phil; Pearce, Charles; Piantadosi, Julia. A new look at urban water storage in a series of connected dams. J. Appl. Probab. 51 (2014), no. 1, 118--135. doi:10.1239/jap/1395771418. https://projecteuclid.org/euclid.jap/1395771418


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