Probability and Expected Time of Emptying of Intermediate Storages under Stochastic Operation

Abstract

A mathematical model for the operation of an intermediate storage under stochastic operational conditions is presented. The material input of the storage occurs at randomly, both in terms of time and amount of material, while the output is of constant volumetric rate. The main practical question is the required initial amount of material in the storage allowing no emptying of storage. In order to determine that we define a two variable function. We develop an equation satisfied by this function and present solution for the case of Erlang(n) distributed inter-arrival time. We provide numerical examples and apply this function for solving the original problem.