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Laplace transform inversion and passage-time distributions in Markov processes

Published online by Cambridge University Press:  14 July 2016

Peter G. Harrison
Peter G. Harrison*
Affiliation:
Imperial College, London
*
∗Postal address: Department of Computing, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK.
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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

ANALYTICAL INVERSION OF LAPLACE TRANSFORMSTIME DELAY DENSITYCYCLE TIMERESPONSE TIMEQUEUEING NETWORKS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 74 - 87
Copyright
Copyright © Applied Probability Trust 1990 

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