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We consider modulated Poisson--Voronoi tessellations, intended as models for telecommunication networks on a nationwide scale. By introducing an algorithm for the simulation of the typical cell of the latter tessellation, we lay the mathematical foundation for such a global analysis. A modulated Poisson--Voronoi tessellation has an intensity which is spatially variable and, hence, is able to provide a broad spectrum of model scenarios. Nevertheless, the considered tessellation model is stationary and we consider the case where the modulation is generated by a Boolean germ-grain model with circular grains. These circular grains may either have a deterministic or random but bounded radius. Furthermore, based on the introduced simulation algorithm for the typical cell and on Neveu's exchange formula for Palm probability measures, we show how to estimate the mean distance from a randomly chosen location to its nearest Voronoi cell nucleus. The latter distance is interpreted as an important basic cost characteristic in telecommunication networks, especially for the computation of more sophisticated functionals later on. Said location is chosen at random among the points of another modulated Poisson process where the modulation is generated by the same Boolean model as for the nuclei. The case of a completely random placement for the considered location is thereby included as a special case. The estimation of the cost functional is performed in a way such that a simulation of the location placement is not necessary. Test methods for the correctness of the algorithm based on tests for random software are briefly discussed. Numerical examples are provided for characteristics of the typical cell as well as for the cost functional. We conclude with some remarks about extensions and modifications of the model regarded in this paper, like modulated Poisson--Delaunay tessellations.

A novel modulating scheme is presented that improves echo path modelling using system identification techniques in noise contaminated environments. The systems of interest are usually based on a class of digital adaptive filters (DAFs). A novel chaotic based modulation regime utilising the logistic mapping is exploited to whiten the speech power spectral density (PSD) whilst preserving the signal bandwidth requirements. Software simulations are reported for noise-impaired and noise-free circuits. In the noise-free configuration, it is shown that the described modulation scheme significantly improves the convergence rate and guarantees optimal modelling independent of the input speech signal statistics. In the noise contaminated environment, it is shown that stringent operating requirements dictate modelling with echo to noise ratios approaching 0 dB. Uncoded speech is shown to be ineffective in driving the models when noise to echo ratios exceed approximately -10 dB. The noise-impaired environment may invalidate speech driven DAF circuits, however, it is shown that the chaotic coding improves the signal energy and whitens the resultant PSD. As a result, it is demonstrated that the proposed coding scheme allows accurate DAF modelling for noise levels that are 40 dB higher than the corrupted uncoded speech case. Furthermore, it is shown that for a practical range of noise conditions the proposed coding results in a faster convergence rate than the upper bound established for the noiseless uncoded case.

Many practical large-scale optimization problems are not only sparse, but also display some form of block-structure such as primal or dual block angular structure. Often these structures are nested: each block of the coarse top level structure is block-structured itself. Problems with these characteristics appear frequently in stochastic programming but also in other areas such as telecommunication network modelling.

Domain-specific modelling (DSM) environments enable experts in a certain domain to actively participate in model-driven development. Developing DSM environments need to be cost-efficient, since they are only used by a limited group of domain experts. Different model-driven technologies promise to allow this cost-efficient development. [1] presented experiences in developing a DSM environment for telecommunication network modelling. There, challenges were identified that need to be addressed by other new modelling technologies. In this paper, we now present the results of addressing one of theses challenges—abstraction and reuse support—with the Reuseware Composition Framework. We show how we identified the abstraction and reuse features required in the telecommunication DSM environment in a case study and extended the existing environment with these features using Reuseware. We discuss the advantages of using this technology and propose a process for further improving the abstraction and reuse capabilities of the DSM environment in the future.