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Fitting of stochastic telecommunication network models via distance measures and Monte–Carlo tests

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Abstract

We explore real telecommunication data describing the spatial geometrical structure of an urban region and we propose a model fitting procedure, where a given choice of different non-iterated and iterated tessellation models is considered and fitted to real data. This model fitting procedure is based on a comparison of distances between characteristics of sample data sets and characteristics of different tessellation models by utilizing a chosen metric. Examples of such characteristics are the mean length of the edge-set or the mean number of vertices per unit area. In particular, after a short review of a stochastic-geometric telecommunication model and a detailed description of the model fitting algorithm, we verify the algorithm by using simulated test data and subsequently apply the procedure to infrastructure data of Paris.

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References

  1. F. Baccelli and B. Blaszczyszyn, On a coverage process ranging from the Boolean model to the Poisson-Voronoi tessellation, Advances in Applied Probability 33 (2001) 293–323.

    Article  Google Scholar 

  2. F. Baccelli, C. Gloaguen and S. Zuyev, Superposition of planar Voronoi tessellations, Communications in Statistics, Series Stochastic Models 16 (2000) 69–98.

    Article  Google Scholar 

  3. F. Baccelli, M. Klein, M. Lebourges and S. Zuyev, Géométrie aléatoire et architecture de réseaux, Annales des Télécommunications 51 (1996) 158–179.

    Google Scholar 

  4. F. Baccelli, D. Kofman and J.L. Rougier, Self organizing hierarchical multicast trees and their optimization, Proceedings of IEEE Infocom ’99 (1999) 1081–1089, New York.

  5. F. Baccelli and S. Zuyev, Poisson-Voronoi spanning trees with applications to the optimization of communication networks, Operations Research 47 (1996) 619–631.

    Article  Google Scholar 

  6. A.J. Baddeley and E.B. Vedel Jensen, Stereology for statisticians. Chapman & Hall 2004.

  7. C. Gloaguen, P. Coupé, R. Maier and V. Schmidt, Stochastic modelling of urban access networks, in: Proc. 10th Internat. Telecommun. Network Strategy Planning Symp., (Munich, June 2002), VDE, Berlin (2002) pp. 99–104.

  8. C. Gloaguen, F. Fleischer, H. Schmidt and V. Schmidt, Simulation of typical Cox-Voronoi cells, with a special regard to implementation tests.Mathematical Methods of Operations Research 62 (2005a) to appear.

  9. C. Gloaguen, F. Fleischer, H. Schmidt and V. Schmidt, Analysis of shortest paths and subscriber line lengths in telecommunication access networks. Working paper, under preparation (2005b).

  10. L. Heinrich, H. Schmidt and V. Schmidt, Central limit theorems for Poisson hyperplane tessellations. Preprint, (2005) submitted.

  11. R. Maier, Iterated Random Tessellations with Applications in Spatial Modelling of Telecommunication Networks. Doctoral Dissertation, University of Ulm 2003.

  12. R. Maier, J. Mayer and V. Schmidt, Distributional properties of the typical cell of stationary iterated tessellations, Mathematical Methods of Operations Research 59 (2004) 287–302.

    Article  Google Scholar 

  13. R. Maier and V. Schmidt, Stationary iterated tessellations, Advances in Applied Probability 35 (2003) 337–353.

    Article  Google Scholar 

  14. J. Mayer, V. Schmidt and F. Schweiggert, A unified simulation framework for spatial stochastic models, Simulation Modelling Practice and Theory 12 (2004) 307–326.

    Article  Google Scholar 

  15. J. Møller, Random tessellations in ď. Advances in Applied Probability 21 (1989) 37–73.

    Google Scholar 

  16. J. Ohser and F. Mücklich, Statistical Analysis of Microstructures in Materials Science. J. Wiley & Sons, Chichester, 2000.

    Google Scholar 

  17. A. Okabe, B. Boots, K. Sugihara and S.N. Chiu, Spatial Tessellations. 2nd ed., J.Wiley & Sons, Chichester (2000).

    Book  Google Scholar 

  18. R. Schneider and W. Weil. Stochastische Geometrie. Teubner, Stuttgart 2000.

  19. J. Serra, Image Analysis and Mathematical Morphology. Academic Press, London. (1982).

    Google Scholar 

  20. P. Soille, Morphological Image Analysis. Springer, Berlin (2003).

    Google Scholar 

  21. D. Stoyan, W.S. Kendall and J. Mecke, Stochastic geometry and its applications. 2nd ed., J. Wiley & Sons, Chichester 1995.

    Google Scholar 

  22. D. Stoyan and H. Stoyan, Fractals, Random Shapes and Point Fields, Methods of Geometrical Statistics. J. Wiley & Sons, Chichester 1994.

    Google Scholar 

  23. K. Tchoumatchenko and S. Zuyev, Aggregate and fractal tessellations, Probability Theory Related Fields 121 (2001) 198–218.

    Article  Google Scholar 

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Gloaguen, C., Fleischer, F., Schmidt, H. et al. Fitting of stochastic telecommunication network models via distance measures and Monte–Carlo tests. Telecommun Syst 31, 353–377 (2006). https://doi.org/10.1007/s11235-006-6723-3

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  • DOI: https://doi.org/10.1007/s11235-006-6723-3

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