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A laplace transform representation in a class of renewal queueing and risk processes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Gordon E. Willmot
Gordon E. Willmot*
Affiliation:
University of Waterloo
*
∗Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
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Abstract

For a class of renewal queueing processes characterized by a rational Laplace–Stieltjes transform of the arrival inter-occurrence time distribution, the Laplace–Stieltjes transform of the equilibrium (actual) waiting time distribution is re-expressed in a manner which facilitates explicit inversion under certain conditions. The results are of interest in other contexts as well, as for example in insurance ruin theory. Various analytic properties of these quantities are then obtained as a result.

Keywords

Compound geometricfailure rateresidual lifetimesubexponentialregular variationErlang distributionCoxian distributionLagrange interpolation

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 570 - 584
Copyright
Copyright © Applied Probability Trust 1999 

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