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An Introduction to Numerical Transform Inversion and Its Application to Probability Models
TLDR
Historically, transforms were exploited extensively for solving queueing and related probability models, but only rarely was numerical inversion attempted, and transforms became regarded more as mathematical toys than practical tools.
Diversity ALOHA - A Random Access Scheme for Satellite Communications
TLDR
A generalization of the slotted ALOHA random access scheme is considered in which a user transmits multiple copies of the same packet and it is found that under light traffic, multiple transmission gives better delay performance.
On the Laguerre Method for Numerically Inverting Laplace Transforms
TLDR
A new variant of the Laguerre method is presented based on using a previously developed version of the Fourier-series method to calculate the coefficients of theLaguerrre generating function, developing systematic methods for scaling, and using Wynn's (epsilon)-algorithm to accelerate convergence of the Higgs boson series when the LAGs do not converge to zero geometrically fast.
Waiting-time tail probabilities in queues with long-tail service-time distributions
TLDR
Algorithms for computing the waiting-time distribution by Laplace transform inversion when the Laplace transforms of the interarrival-time and service-time distributions are known are developed and a convenient two-parameter family of long-tail distributions on the positive half line with explicit Laplace transformations is introduced.
Squeezing the Most Out of ATM
TLDR
An exact numerical algorithm is developed that shows that the effective-bandwidth approximation can overestimate the target small blocking probabilities by several orders of magnitude when there are many sources that are more bursty than Poisson.
Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times
TLDR
Numerical examples show that the exponential approximations for tail probabilities of the steady-state waiting time in infinite-capacity multiserver queues based on small-tail asymptotics are remarkably accurate, especially for higher percentiles, such as the 90th percentile and beyond.
Asymptotics for steady-state tail probabilities in structured markov queueing models
We apply Tauberian theorems with known transforms to establish asymptotics for the basic steady-state distributions in the BMAP/G/l queue. The batch Markovian arrival process (BMAP)is equivalent to
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