Résumé en anglais

The modeling of mobile networks is difficult because of the number of users and their mobilities. In this study, we present a new methodology based upon stochastic ordering of Markov chains in order to evaluate the performance measures in wireless networks. These kind of networks are based on cellular systems. The cellular systems use different frequency coverage in order to increase system capacity. During a communication, a user may move from one cell to another which is named the handover. We propose to compute the dropping handover probabilities. The system is represented by a continuous time Markov chain which is too large to be solved by a numerical method. Our approach is to define a new Markov chain with a smaller state space size, and which provides an upper bound for the dropping handover probabilities. We define an aggregation process based on the weak stochastic orderings in order to define the aggregated upper Markov chain. We have proved using the stochastic comparison that the aggregatedMarkov chain provides an upper bound for the dropping handover probabilities.