First exit times and diffusion approximations for storage models with Poisson inputs, Poisson outputs and deterministic release rule

In this paper we discuss a number of finite storage problems with random inputs and random outputs together with linear release policy. This class of problems forms one dimensional master equations with separable kernel. For this class of problems the first passage time for overflow or emptiness can...

Full description

Saved in:
Bibliographic Details
Published in:Opsearch 2013-12, Vol.50 (4), p.566-581
Main Authors: Vittal, P. R., Venkateswaran, M., Reddy, P. R. S.
Format: Article
Language:English
Subjects:
Analysis
Approximation
Business and Management
Differential equations
Inventory management
Laplace transforms
Management
Mathematics
Operations Research/Decision Theory
Ordinary differential equations
Probability
Random variables
Storage
Studies
Theoretical Article
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we discuss a number of finite storage problems with random inputs and random outputs together with linear release policy. This class of problems forms one dimensional master equations with separable kernel. For this class of problems the first passage time for overflow or emptiness can be transformed into ordinary differential equations. Closed form analytical solutions are obtained for first passage times for emptiness and overflow, treating the barriers as absorbing or reflecting. The imbedding technique is used to obtain the closed form solution for all the models. The results are derived in the form of third order differential equations for Laplace Transform functions for the first passage times. Diffusion approximation for these models is also obtained using suitable statistical conditions.
ISSN:0030-3887
0975-0320
DOI:10.1007/s12597-013-0127-4