On a random variable associated with excursions in an M/M/\infty system
Queueing Systems: Theory and Applications
Asymptotic Expansions for the Congestion Period for the M/M/∞ Queue
Queueing Systems: Theory and Applications
Two-Class Priority Queueing System with State-Dependent Arrivals
Queueing Systems: Theory and Applications
A truncated Pareto distribution
Computer Communications
Short Communication: A truncated bivariate generalized Pareto distribution
Computer Communications
A Stochastic Model for Order Book Dynamics
Operations Research
Transient analysis of a queue with system disasters and customer impatience
Queueing Systems: Theory and Applications
Time-dependent analysis of a single-server retrial queue with state-dependent rates
Operations Research Letters
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It is often possible to effectively calculate probability density functions (pdf's) and cumulative distribution functions (cdf's) by numerically inverting Laplace transforms. However, to do so it is necessary to compute the Laplace transform values. Unfortunately, convenient explicit expressions for required transforms are often unavailable for component pdf's in a probability model. In that event, we show that it is sometimes possible to find continued-fraction representations for required Laplace transforms that can serve as a basis for computing the transform values needed in the inversion algorithm. This property is very likely to prevail for completely monotone pdf's, because their Laplace transforms have special continued fractions called S fractions, which have desirable convergence properties. We illustrate the approach by considering applications to compute first-passage-time cdfs in birth-and-death processes and various cdf's with non-exponential tails, which can be used to model service-time cdf's in queueing models. Included among these cdf's is the Pareto cdf.