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

This paper proposes a framework to analyze a wireless architecture where vehicles collect data from devices. Roads and vehicles are modeled by a Poisson line process and a Cox point process, respectively. At any given time, each 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 these direct communications from roadside devices to vehicles by investigating the network performance in both space and time domains. For the space domain analysis, we explicitly derive the signal-to-interference ratio distribution of the typical vehicle and the area spectral efficiency of the proposed network. For the time domain analysis, we characterize the evolution of the area fraction of the coverage disks over time and then evaluate the minimum association delay of the proposed network by deriving the distribution of the minimum time required for an arbitrarily located roadside device to be covered by a disk. Leveraging the derived network performance, we investigate the optimization of network utility functions given by linear combinations of the performance metrics.