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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.