Numerical Inversion of Laplace Transforms Using Laguerre Functions
Journal of the ACM (JACM)
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
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Packet switching networks lead mostly to M/GI/1 queue models. In this paper, computing methods are designed in order to get quickly approximate values for response time of these networks. Laplace transform is a powerful tool to study such queuing systems. But inversion of the Laplace transform on the real line is well known to be an ill-conditioned problem and usual numerical methods of inversion fail to give accurate error bounds. A new method to address this old problem is afforded by the recently developed formal computing tools: exact computations can be done during the first steps of calculation, while usual floating point computations remain confined to the last steps. Applying that method to an M/GI/1 queue, a formal approach is designed, leading to proven bounds, and several numerical improvements are proposed. Accurate bounds are obtained.