New Directions into the Stochastic Geometry Analysis of Dense CSMA Networks

We consider extended wireless networks characterized by a random topology of access points (APs) contending for medium access over the same wireless channel. Recently, stochastic geometry has emerged as a powerful tool to analyze random networks adopting MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows considering also random fading on each link. In this paper, we extend previous stochastic geometry models of CSMA networks, developing computationally efficient techniques to obtain throughput distributions, in addition to spatial averages, which permit us to get interesting insights into the impact of protocol parameters and channel variability on the spatial fairness among the nodes. Moreover, we extend the analysis to a significant class of topologies in which APs are not placed according to a Poisson process.