Modélisation markovienne du trafic dans les réseaux de communication

The principal question we address in this work is the following: "Is Markov modelling appropriate to analyse data networks?". We will conclude that it is. The motivation for this question comes from the work of a research team at Bellcore who argue that the models used in teletraffic engineering are questionnable. Their argument is based on long measurements performed on their local network. Their results, with the major conclusion that the traffic is self-similar, have shaken the teletraffic community. After having exposed the principal characteristics of the Markovian model, we analyse measurements done on the EPFL network and on the Bellcore network. The results of the analysis lead us to suspect the suitability of Markovian models. Therefore, we study the interworking unit Ethernet/DQDB considering a network totally loaded. No hypothesis is made for the traffic profile, yet the study leads to strong conclusions and we therefore try to understand the queue behavior with the spectral analysis in order to better characterize the data traffic. The next step consists of reproducing the self-similarity observed in the data traffic with modulated Markov chains. Here, Courtois's theory of decomposability is used. We have shown that it is possible to reproduce self-similarity on a finite timescale, but that the number of parameters needed to manipulate in the modulated Markov remains large. In the next step, we propose a technique to reduce them drastically. A method of finding a Markov modulated chain as a function of the expectation, the local Hurst parameter and the domain where the process exhibits self-similarity has been developed. Finally, we analyse the statistical multiplexing in a new ATM architecture by comparing the multiplexing of VBR sources (with a modulated Markovian chains) on a CBR and on a VBR connection, using the above techniques.

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