On the statistical characterization of the binomial line processes

Abstract

This thesis introduces the Binomial Line Process (BLP) and then Binomial Line Cox Process (BLCP) based on BLP, a novel spatial stochastic model for the charac- terization of streets in the statistical evaluation of wireless and vehicular networks. Stochastic Geometry based network planning is an extensively studied area. Ex- isting models for streetwise millimeter wave network implementation include Pois- son line processes (PLP), Manhattan line processes (MLP), etc. However, all of these models lack an essential aspect of city-wide street network planning: street density is denser in the city center and sparse near the suburbs. These models simulate street networks by uniformly distributing the roads on the entire R 2 plane. Contrary to these models, the BLP model introduced here restricts the origin of the roads to a fixed circular area centered at the origin of the Euclidean plane, thereby artificially introducing inhomogeneity in street density with respect to the distance from the center. The idea being the further away we go from the city center, i.e., towards the suburbs, the sparser the entire network becomes. We have derived a closed-form expression for the contact distribution of the BLP from a random location on the plane. Leveraging this, we introduced the novel Binomial line Cox process (BLCP) to emulate points on individual lines of the BLP, where we derive the distribution of the distance of the nearest point of the Poisson line Cox process (PLCP) and the Probability Generating Functional (PGFL) of the PLCP. Based on the PGFL and the nearest point distribution, we characterize the Signal to Interference plus Noise Ratio (SINR) coverage of a network. Using these numerical results, we highlight that the network coverage characteristics from the perspective of a user at city center is remarkably different to that of a suburban user. This framework can be integrated with the existing models of line processes for a more accurate characterization of streets in urban and suburban environments.