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

Gordon E. Willmot

35 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

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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References

1997Modelling Extremal Events 1987Applied Probability and Queues 1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.1987Stochastic Modelling and Analysis: A Computational Approach.2023Advances in Queueing Theory, Methods, and Open Problems 1989Subexponential distributions and characterizations of related classes 1999Analysis of a defective renewal equation arising in ruin theory 1983A property of the generalized inverse Gaussian distribution with some applications

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