Investigation of operation of intermediate storages applying probability density functions satisfying linear differential equation

Abstract

In this paper operation of a batch/continuous processing system connected by an intermediate storage is considered. The filling process is supposed to be random and the output process is deterministic, consequently the process in the storage is a stochastic process. We investigate the problem of determination of necessary initial amount of material to avoid emptying of the storage. We define a function which is able to handle together the probability and expected time to shortage. We set up an integral equation for it, and in a special case of density functions of inter-arrival times we transform to an integro-differential equation. We provide analytical formula for the solution. We compare the analytical solution to the results arising from Monte-Carlo simulations. In some cases we use only the form of the analytical solution but coefficients are determined by parameter fitting. Finally we use the computed functions to determine the necessary initial amount of material to a given reliability level.