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

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

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Article ID: iaor20013001
Country: United Kingdom
Volume: 36
Issue: 2
Start Page Number: 570
End Page Number: 584
Publication Date: Jun 1999
Journal: Journal of Applied Probability
Authors:
Keywords: risk
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.

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