Binomial Line Processes: Distance Distributions

TL;DR

This paper introduces the binomial line process (BLP), a new spatial model for city streets that accounts for inhomogeneity by varying street density with distance from the city center, and derives related distance distributions.

Contribution

The paper presents the BLP as a novel inhomogeneous street model and derives its contact distribution, extending stochastic geometry tools for urban network analysis.

Findings

BLP captures inhomogeneity of city streets with distance from center.

Derived closed-form contact distribution for BLP.

Spatial configurations differ significantly between city center and suburbs.

Abstract

We introduce the binomial line process (BLP), a novel spatial stochastic model for the characterization of streets in the statistical evaluation of wireless and vehicular networks. Existing stochastic geometry models for streets, e.g., Poisson line processes (PLP) and Manhattan line processes (MLP) lack an important aspect of city-wide street networks: streets are denser in the city center and sparse near the suburbs. Contrary to these models, the BLP restricts the generating points of the streets to a fixed radius centered at the origin of the Euclidian plane, thereby capturing the inhomogeneity of the streets with respect to the distance from the center. We derive a closed-form expression for the contact distribution of the BLP from a random location on the plane. Leveraging this, we introduce the novel Binomial line Cox process (BLCP) to emulate points on individual lines of the BLP and derive the distribution to the nearest BLCP point from an arbitrary location. Using numerical results, we highlight that the spatial configuration of the streets is remarkably distinct from the perspective of a city center user to that of a suburban user. The framework developed in this paper can be integrated with the existing models of line processes for more accurate characterization of streets in urban and suburban environments.