## Multidimensional transform inversion with applications to the transient $$M/G/1$$ queue.(English)Zbl 0808.65140

From the authors’ summary: “We develop an algorithm for numerically inverting multidimensional transforms. Our algorithm applies to any number of continuous variables (Laplace transforms) and discrete variables (generating functions). We use the Fourier-series method; that is, the inversion formula is the Fourier series of a periodic function constructed by aliasing”.
The algorithm can apply to compute probability distributions of interest in queueing models. Among other numerical examples, the authors employ their algorithm to invert the classical double transform expressions for the time-dependent transient queue-length and workload distributions in the $$M/G/1$$ queue.

### MSC:

 65R10 Numerical methods for integral transforms 65T40 Numerical methods for trigonometric approximation and interpolation 65C99 Probabilistic methods, stochastic differential equations 44A10 Laplace transform 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 60K25 Queueing theory (aspects of probability theory)
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