# Spatial and Temporal Analysis of Direct Communications from Static Devices to Mobile Vehicles

## TL;DR

This paper introduces a stochastic geometry-based framework to analyze the spatial and temporal performance of vehicle-to-device communication networks, focusing on coverage, interference, latency, and network optimization.

## Contribution

It develops a novel analytical model combining Poisson point processes and Cox processes to evaluate short-term and long-term network behaviors.

## Key findings

- Derived the SIR distribution for typical vehicles.
- Calculated the area spectral efficiency of the network.
- Analyzed latency and coverage trade-offs.

## Abstract

This paper proposes a framework to analyze an emerging wireless architecture where vehicles collect data from devices. Using stochastic geometry, the devices are modeled by a planar Poisson point process. Independently, roads and vehicles are modeled by a Poisson line process and a Cox point process, respectively. For any given time, a vehicle is assumed to communicate with a roadside device in a disk of radius $ \nu $ centered at the vehicle, which is referred to as the coverage disk. We study the proposed network by analyzing its short-term and long-term behaviors based on its space and time performance metrics, respectively. As short-term analysis, we explicitly derive the signal-to-interference ratio distribution of the typical vehicle and the area spectral efficiency of the proposed network. As long-term analysis, we derive the area fraction of the coverage disks and then compute the latency of the network by deriving the distribution of the minimum waiting time of a typical device to be covered by a disk. Leveraging these properties, we analyze various trade-off relationships and optimize the network utility. We further investigate these trade-offs using comparison with existing cellular networks.