Analyzing Wireless Networks Using Binomial Line Cox Processes

The stochastic geometry analysis of vehicular networks and on-street deployment of base stations is largely based on Cox processes driven by Poissonian models. In this paper, we investigate scenarios where a model with a finite and deterministic number of streets, termed the binomial line process (BLP), is more accurate. We characterize the statistical properties of the BLP and the corresponding binomial line Cox process (BLCP). We derive the line length density and the intersection density for the BLP and demonstrate how it models the inhomogeneity of the streets in a city. Finally, leveraging the derived framework, we analyze the performance of a network whose access points are deployed along the streets of a city. Our study captures the variation in the service performance of the users across different locations of a city and thus it leads to key network planning and dimensioning rules for the operators.