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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 

References

Archibald, T. W., McKinnon, K. I. M. and Thomas, L. C. (1997). An aggregate stochastic dynamic programming model of multireservoir systems. Water Resources Res. 33, 333–340.Google Scholar
Archibald, T. W., McKinnon, K. I. M. and Thomas, L. C. (2006). Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming. Naval Res. Logistics 53, 217–225.Google Scholar
Archibald, T. W., Buchanan, C. S., Thomas, L. C. and McKinnon, K. I. M. (2001). Controlling multi-reservoir systems. Europ. J. Operat. Res. 129, 619–626.CrossRefGoogle Scholar
Cohen, M. J. and Brown, M. T. (2007). A model examining hierarchical wetland networks for watershed stormwater management. Ecological Modelling 201, 179–193.Google Scholar
Gani, J. (1969). Recent advances in storage and flooding theory. Adv. Appl. Prob. 1, 90–110.CrossRefGoogle Scholar
Gaver, D. P., Jacobs, P. A. and Latouche, G. (1984). Finite birth-and-death models in randomly changing environments. Adv. Appl. Prob. 16, 715–731.Google Scholar
Howlett, P. and Piantadosi, J. (2009). An application of the pump-to-fill policy for management of urban stormwater. Environ. Modeling Assessment 14, 195–207.CrossRefGoogle Scholar
Latouche, G. and Ramaswami, V. (1999). Introduction to Matrix Analytic Methods in Stochastic Modeling. Society for Industrial and Applied Mathematics, Philadelphia, PA.CrossRefGoogle Scholar
Latouche, G., Jacobs, P. A. and Gaver, D. P. (1984). Finite Markov chain models skip-free in one direction. Naval Res. Logistics Quart. 31, 571–588.Google Scholar
Moran, P. A. P. (1954). A probability theory of dams and storage systems. Austral. J. Appl. Sci. 5, 116–124.Google Scholar
Moran, P. A. P. (1959). The Theory of Storage. Methuen, London.Google Scholar
Neuts, M. F. (1981). Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD.Google Scholar
Neuts, M. F. (1989). Structured Stochastic Matrices of M/G/1 Type and Their Applications. Marcel Dekker, New York.Google Scholar
Pearce, C. E. (2009). Optimal stormwater management with two dams: the dynamics of the pump-to-fill policy. Optimization 58, 181–192.CrossRefGoogle Scholar
Pearce, C. E. M., Piantadosi, J. and Howlett, P. G. (2007). On an optimal control policy for stormwater management in two connected dams. J. Industrial Manag. Optimization 3, 313–320.CrossRefGoogle Scholar
Piantadosi, J. (2004). Optimal policies for storage of urban stormwater. , University of South Australia. Available at http://arrow.unisa.edu.au:8081/1959.8/82105.Google Scholar
Piantadosi, J., Howlett, P. G., Bean, N. G. and Beecham, S. (2010). Modelling systems of reservoirs using structured Markov chains. Proc. Inst. Civ. Eng. Water Manag. 163, 407–416.CrossRefGoogle Scholar
Rosenberg, K., Boland, J. and Howlett, P. G. (2004). Simulation of monthly rainfall totals. ANZIAM J. 46, E85–E104.Google Scholar
Thomas, P., Howlett, P. G. and Piantadosi, J. (2010). Investigating the optimal management of the Helps Road drain urban stormwater harvesting system within the city of Salisbury. Europ. Water 29, 11–19.Google Scholar
Yeo, G. F. (1974). A finite dam with exponential release. J. Appl. Prob. 11, 122–133.CrossRefGoogle Scholar
Yeo, G. F. (1975). A finite dam with variable release rate. J. Appl. Prob. 12, 205–211.Google Scholar