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Contributions of Alladi Ramakrishnan to the Mathematical Sciences Read chapter Read first chapter

2010 | OriginalPaper | Chapter

Storage Models for a Class of Master Equations with Separable Kernels

Authors : P. R. Vittal, S. Jayasankar, V. Muralidhar

Published in: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Publisher: Springer New York

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Summary

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.

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previous chapter Connections Between Bernoulli Strings and Random Permutations
next chapter Inverse Consistent Deformable Image Registration
Footnotes
1
This work was completed when one of the authors (P.R. Vittal) was in ISI (Bangalore) in January 2009.
 
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Metadata
Title
Storage Models for a Class of Master Equations with Separable Kernels
Authors
P. R. Vittal
S. Jayasankar
V. Muralidhar
Copyright Year
2010
Publisher
Springer New York
Book
The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Print ISBN: 978-1-4419-6262-1

Electronic ISBN: 978-1-4419-6263-8

Copyright Year: 2010

DOI
https://doi.org/10.1007/978-1-4419-6263-8_25

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