## Section: New Results

### Performance analysis of cellular networks with opportunistic scheduling using queueing theory and stochastic geometry

In [38] submitted this year, combining stochastic geometric approach with some classical results from queuing theory,we propose a comprehensive framework for the performance study of large cellular networks featuring opportunistic scheduling. Rapid and verifiable with respect to real data, our approach is particularly useful for network dimensioning and long term economic planning. It is based on a detailed network model combining an information-theoretic representation of the link layer, a queuing-theoretic representation of the users' scheduler, and a stochastic-geometric representation of the signal propagation and the network cells. It allows one to evaluate principal characteristics of the individual cells, such as loads (defined as the fraction of time the cell is not empty), the mean number of served users in the steady state, and the user throughput. A simplified Gaussian approximate model is also proposed to facilitate study of the spatial distribution of these metrics across the network. The analysis of both models requires only simulations of the point process of base stations and the shadowing field to estimate the expectations of some stochastic-geometric functionals not admitting explicit expressions. A key observation of our approach , bridging spatial and temporal analysis, relates the SINR distribution of the typical user to the load of the typical cell of the network. The former is a static characteristic of the network related to its spectral efficiency while the latter characterizes the performance of the (generalized) processor sharing queue serving the dynamic population of users of this cell.