# American Institute of Mathematical Sciences

April  2007, 3(2): 279-292. doi: 10.3934/jimo.2007.3.279

## Management of water storage in two connected dams

 1 Centre for Industrial and Applied Mathematics, Mawson Lakes Campus, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, 5095, Australia, Australia, Australia

Received  September 2006 Revised  February 2007 Published  April 2007

We consider the management of urban stormwater in two connected dams. Stormwater generated by local rainfall flows into a large capture dam and is subsequently pumped to a smaller supply dam. We assume random supply and constant demand. A simple management policy is to pump as much water as possible each day from the capture dam to the supply dam without allowing the supply dam to overflow. If there is insufficient water in the supply dam to meet the desired daily demand then all water in the supply dam is used. The policy defines a large block transition matrix with repeating entries. We use Matrix Analytic Methods to decompose the event space for the various state transitions and subsequently construct simplified equations for the invariant state probability vector. In this way we enable an elementary solution procedure to find the invariant probability. This paper extends previous work by Piantadosi [12] by allowing higher levels of demand and prefaces more recent work by Piantadosi et al [13].
Citation: Phil Howlett, Julia Piantadosi, Paraskevi Thomas. Management of water storage in two connected dams. Journal of Industrial & Management Optimization, 2007, 3 (2) : 279-292. doi: 10.3934/jimo.2007.3.279
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