## Section: New Results

### Evaluation and optimization of the quality of service perceived by mobile users for new services in cellular networks

The goal of this thesis[1] defended in 2015 is to develop tools and methods for the evaluation of the QoS (Quality of Service) perceived by users, as a function of the traffic demand, in modern wireless cellular networks. This complex problem, directly related to network dimensioning, involves modeling dynamic processes at several time-scales, which due to their randomness are amenable to probabilistic formalization. Firstly, on the ground of information theory, we capture the performance of a single link between a base station and a user in the context of a cellular network with orthogonal channels and MIMO technology. We prove and use some lower bounds of the information-theoretic ergodic capacity of such a link, which account also for the fast channel variability caused by multi-path propagation. These bounds give robust basis for further user QoS evaluation. Next, one considers several (possibly mobile) users, arriving in the network and requesting some service from it. We consider variable (elastic) bit-rate services, in which transmissions of some amounts of data are realized in a best-effort manner, or constant bit-rate services, in which a certain transmission rate needs to be maintained during requested times. On the ground of queuing theory, one captures this traffic demand and service process using appropriate (multi-class) processor sharing (PS) or loss models. In this thesis, we adapt existing PS models and develop a new loss model for wireless streaming traffic, in which the aforementioned information-theoretic capacities of single links describe the instantaneous user service rates. The multi-class models are used to capture the spatial heterogeneity of user channels, which depends on the user geographic locations and propagation shadowing phenomenon. Finally, on top of the queueing-theoretic processes, one needs to consider a multi-cellular network, whose base stations are not necessarily regularly placed, and whose geometry is further perturbed by the shadowing phenomenon. We address this randomness aspect by using some models from stochastic geometry, notably Poisson point processes and Palm formalism applied to the typical cell of the network. Applying the above three-fold approach, supposed to represent all crucial mechanisms and engineering parameters of cellular networks (such as LTE), we establish some macroscopic relations between the traffic demand and the user QoS metrics for some elastic and constant bit-rate services. These relations are mostly obtained in a semi-analytic way, i.e., they only involve static simulations of a Poisson point process (modeling the locations of base stations) in order to evaluate its characteristics which are not amenable to analytic expressions. More precisely, regarding the data traffic (the elastic bit-rate service), we capture the inter-cell interference, making the PS queue models of individual cells dependent, via some system of cell-load equations. These equations allow one to determine the mean user throughput, the mean number of users and the mean cell load in a large network, as a function of the traffic demand. The spatial distribution of these QoS metrics in the network is also studied. We validate our approach by comparing the obtained results with those measured from live-network traces. We observe a remarkably good agreement between the model predictions and the statistical data collected in several deployment scenarios. Regarding constant bit-rate services, we propose a new stochastic model to evaluate the frequency and the number of interruptions during real-time streaming calls in function of user radio conditions. Despite some fundamental similarities with the classical Erlang loss model, a more adequate model was required for in this case, where the denial of service is not definitive for a given call: it takes the form of, hopefully short, interruptions or outage periods. Our model allows one to take into account realistic implementations of the considered streaming service. We use it to study the quality of service metrics in function of user radio conditions in LTE networks. All established results contribute to the development of network dimensioning methods and are currently used in Orange internal tools for network capacity calculations.