Abstract
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.
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Keywords
- Sojourn Time
- Numerical Inversion
- Response Time Distribution
- Piecewise Polynomial Function
- Packet Switching Network
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© 2000 Springer-Verlag Berlin Heidelberg
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Douillet, P.L., Beylot, AL., Becker, M. (2000). Computing Stochastical Bounds for the Tail Distribution of an M/GI/1 Queue. In: Pujolle, G., Perros, H., Fdida, S., Körner, U., Stavrakakis, I. (eds) Networking 2000 Broadband Communications, High Performance Networking, and Performance of Communication Networks. NETWORKING 2000. Lecture Notes in Computer Science, vol 1815. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45551-5_36
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DOI: https://doi.org/10.1007/3-540-45551-5_36
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