THE BOTTOMLESS DAM WITH SEASONAL INPUTS

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Abstract
Summary: The stationary distribution of the depletion (from the maximum content) of a bottomless dam is derived for the case where the inputs and releases are seasonal. The method used is an extension of the method of Wishart for a problem in queueing theory (without involving seasonality). A numerical example is given illustrating the method for the case of two seasons.In some recent work on dams (see Phatarfod, 1979; Pakes & Phatarfod, 1978), it was shown that it was more appropriate to consider the bottomless (or the infinitely deep) dam model rather than the topless (or the infinitely high) dam model as an approximation to the finite dam. The main consideration is that in real‐life reservoir situations, the planned release or draft is almost always less than the mean inflow. It is obvious that with this condition the content of a topless dam will not have a stationary distribution, whereas if we consider the depletion of a dam from its top, this will have a stationary distribution. An additional reason for considering the bottomless dam model is that the model is mathematically more tractable; this property was noticed before for continuous time models (see e.g. Hasofer, 1966)

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