Algorithm 682: Talbot's method of the Laplace inversion problems
ACM Transactions on Mathematical Software (TOMS)
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
ACM Transactions on Mathematical Software (TOMS)
An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates
IEEE/ACM Transactions on Networking (TON)
Numerical inversion of multidimensional Laplace transforms by the Laguerre method
Performance Evaluation
Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform
Journal of the ACM (JACM)
Algorithm 368: Numerical inversion of Laplace transforms [D5]
Communications of the ACM
Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
Comparison of sequence accelerators forthe Gaver method of numerical Laplace transform inversion
Computers & Mathematics with Applications
Numerical Transform Inversion Using Gaussian Quadrature
Probability in the Engineering and Informational Sciences
Future Generation Computer Systems - Systems performance analysis and evaluation
Priority queueing systems: from probability generating functions to tail probabilities
Queueing Systems: Theory and Applications
Waiting-Time Distribution of M/DN/1 Queues Through Numerical Laplace Inversion
INFORMS Journal on Computing
Waiting and sojourn times in a multi-server queue with mixed priorities
Queueing Systems: Theory and Applications
Inverting flow durations from sampled traffic
Proceedings of the 24th International Teletraffic Congress
Boundary particle method for Laplace transformed time fractional diffusion equations
Journal of Computational Physics
Expected Tardiness Computations in Multiclass Priority M/M/c Queues
INFORMS Journal on Computing
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We introduce and investigate a framework for constructing algorithms to invert Laplace transforms numerically. Given a Laplace transform \hat{f} of a complex-valued function of a nonnegative real-variable, f, the function f is approximated by a finite linear combination of the transform values; i.e., we use the inversion formula f(t) \approx f_n (t) \equiv \frac{1}{t} \sum_{k = 0}^{n}\omega_{k}\hat{f}\biggl(\frac{\alpha_{k}}{t}\biggr),\quad 0 where the weights ωk and nodes αk are complex numbers, which depend on n, but do not depend on the transform \hat{f} or the time argument t. Many different algorithms can be put into this framework, because it remains to specify the weights and nodes. We examine three one-dimensional inversion routines in this framework: the Gaver-Stehfest algorithm, a version of the Fourier-series method with Euler summation, and a version of the Talbot algorithm, which is based on deforming the contour in the Bromwich inversion integral. We show that these three building blocks can be combined to produce different algorithms for numerically inverting two-dimensional Laplace transforms, again all depending on the single parameter n. We show that it can be advantageous to use different one-dimensional algorithms in the inner and outer loops.