2007/01/16 by Vyacheslav M. Abramov, Abramov, Vyacheslav M.
Agricultural and Biological Sciences · Mathematics · #40E05 #60K25 #60K30 #90B05 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #Engineering and Agricultural Innovations #FOS: Mathematics #Probability (math.PR) #math.CA #math.PR #msc:40E05 #msc:60K25 #msc:60K30 #msc:90B05
paper · pdf · doi:10.48550/arxiv.math/0701458
18 pages, 1 table. Revision is submitted
openalex publication_date 2007/01/16 · arxiv created 2008/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a dam model, Lupper and Llower are upper and, respectively, lower levels, L = Lupper-Llower is large and if the level of water is between these bounds, then the dam is said to be in a normal state. Passage across lower or upper levels leads to damage. Let J1=j1L and J2=j2L denote the damage costs per time unit of crossing the lower and, correspondingly, upper level where j1 and j2 are given real constants. It is assumed that input stream of water is described by a Poisson process, while the output stream is state dependent. Let Lt denote the level of water in time t, and cLt denote the water cost at level Lt (Llower<Lt≤ Lupper). Assuming that p1=limt→∞P\Lt=Llower\, p2=limt→∞P\Lt>Lupper\ and qi=limt→∞P\Lt=i\ (Llower<i≤ Lupper) exist, the aim of the paper is to choose the parameters of an output stream (specifically defined in the paper) minimizing the long-run expenses J=p1J1+p2J2+∑i=Llower+1^Lupperqici.