Storage models for a class of master equations with separable kernels

Abstract

We discuss a number of storage problems for a class of one-dimensional master equations with separable kernels. For this class of problems, the integral equation for the first overflow or first emptiness can be transformed exactly into ordinary differential equations. Analysis is done with a generalised separable kernel. Using imbedding method, closed form solutions are obtained for the first overflow without or with emptiness in a given time. The first passage time for emptiness without or with overflow in a given time is also obtained. The imbedding technique is also used to study the expected amount of overflow in a given time. Diffusion approximation for this model is also obtained using suitable statistical conditions. © 2010 Springer Science+Business Media, LLC.