On a general storage problem and its approximating solution

Publisher Website
Google Scholar
Abstract
AGI/G/r(x) store is considered with independently and identically distributed inputs occurring in a renewal process, with a general release rater(·) depending on the content. The (pseudo) extinction time, or the content, just before inputs is a Markov process which can be represented by a random walk on and below a bent line; this results in an integral equation of the formgn+1(y) = ∫l(y, w)gn(w)dwwithl(y, w) a known conditional density function. An approximating solution is found using Hermite or modified Hermite polynomial expansions resulting in a Gram–Charlier or generalized Gram–Charlier representation, with the coefficients being determined by a matrix equation. Evaluation of the elements of the matrix involves two-dimensional numerical integration for which Gauss–Hermite–Laguerre integration is effective. A number of examples illustrate the quality of the approximating procedure against exact and simulated results.

This publication has 13 references indexed in Scilit: