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Inverse problems in queueing theory and Internet probing

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Abstract

Queueing theory is typically concerned with the solution of direct problems, where the trajectory of the queueing system, and laws thereof, are derived based on a complete specification of the system, its inputs and initial conditions. In this paper we point out the importance of inverse problems in queueing theory, which aim to deduce unknown parameters of the system based on partially observed trajectories. We focus on the class of problems stemming from probing based methods for packet switched telecommunications networks, which have become a central tool in the measurement of the structure and performance of the Internet. We provide a general definition of the inverse problems in this class and map out the key variants: the analytical methods, the statistical methods and the design of experiments. We also contribute to the theory in each of these subdomains. Accordingly, a particular inverse problem based on product-form queueing network theory is tackled in detail, and a number of other examples are given. We also show how this inverse problem viewpoint translates to the design of concrete Internet probing applications.

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Authors and Affiliations

  1. INRIA, École Normale Supérieure, Équipe TREC, 23 avenue d’Italie, CS 81321, 75214, Paris Cedex 13, France

    F. Baccelli & B. Kauffmann

  2. ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), CUBIN is an affiliated program of National ICT Australia (NICTA), Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia

    D. Veitch

Authors
  1. F. Baccelli
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  2. B. Kauffmann
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  3. D. Veitch
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Corresponding author

Correspondence to F. Baccelli.

Additional information

The work of F. Baccelli and B. Kauffmann is funded in part by the Euro NF Network of Excellence and by the French ANR Cmon project.

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Baccelli, F., Kauffmann, B. & Veitch, D. Inverse problems in queueing theory and Internet probing. Queueing Syst 63, 59 (2009). https://doi.org/10.1007/s11134-009-9150-9

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  • DOI: https://doi.org/10.1007/s11134-009-9150-9

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