Abstract
In many queues associated with data traffic (for example, a buffer at a router), arrival and service distributions are heavy-tailed. A difficulty with analyzing these queues is that heavy-tailed distributions do not generally have closed-form Laplace transforms. A recently proposed method, the Transform Approximation Method (TAM), overcomes this by numerically approximating the transform. This paper investigates numerical issues of implementing the method for simple queueing systems. In particular, we argue that TAM can be used in conjunction with the Fourier-series method for inverting Laplace transforms, even though TAM is a discrete approximation and the Fourier method requires a continuous distribution. We give some numerical examples for an M/G/1 priority queue.
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Shortle, J., Gross, D., Fischer, M.J., Masi, D.M.B. (2003). Numerical Methods for Analyzing Queues with Heavy-Tailed Distributions. In: Anandalingam, G., Raghavan, S. (eds) Telecommunications Network Design and Management. Operations Research/Computer Science Interfaces Series, vol 23. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3762-2_10
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DOI: https://doi.org/10.1007/978-1-4757-3762-2_10
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