Computing Publications

Publications Home » Laplace Transform Inversion and P...

Laplace Transform Inversion and Passage-Time Distributions in Markov Processes

Peter G. Harrison

Journal Article
Journal of Applied Probability
Volume 27
Issue 1
pp.74–87
March, 1990
Applied Probability Trust
DOI 10.2307/3214596
Abstract

Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The formula for these inversions is expressed both as an explicit sum and in terms of a recurrence relation which is better suited to numerical computation. The recurrence for the inversion of certain weighted sums of these transforms is then solved by converting it into a linear first-order partial differential equation. The result may be used to find the density function of passage times between states in a Markov process and it is applied to derive an expression for cycle time distribution in tree-structured Markovian queueing networks.

Keywords
AESOP
PDF of full publication (337 kilobytes)
(need help viewing PDF files?)
BibTEX file for the publication
N.B.
Conditions for downloading publications from this site.
 

pubs.doc.ic.ac.uk: built & maintained by Ashok Argent-Katwala.