## Section: New Results

### Spatial Disparity of QoS Metrics Between Base Stations in Wireless Cellular Networks

This work contributes to the line of research on the development of analytic tools for the QoS evaluation and dimensioning of operator cellular networks which is the subject of long-term collaboration between TREC/DYOGENE and Orange Labs (cf Section 8.1.1). Our focus in [8] is to explicitly characterize the disparity of quality of service (QoS) metrics between base stations in large heterogeneous wireless cellular networks. The considered QoS metrics are cell load, users' number, and user throughput. The spatial disparity of these metrics is due to the irregularity of the cells' geometry. In order to consider these irregularities, we assume a Poisson point process of base station locations, random transmission powers, and log-normal shadowing. The interdependency between the performances of the base stations is characterized by a system of load equations. The typical cell simulation model consists in resolving this system in order to find the loads and then deduce the remaining characteristics for each cell of the network. Using stochastic geometric and queueing theoretic techniques, we define the QoS averages, variances, and distributions. Inspired by the analysis of the typical cell model, several investigations lead us to propose a fully analytic approach, called mean cell model, that approximates the averages, variances, and distributions of these QoS metrics. Numerical experiments show a good agreement between the proposed approximations, simulation results, and real-life network measurements.