Two Dimensional Connectivity for Vehicular Ad-Hoc Networks

TL;DR

This paper develops a probabilistic framework for analyzing two-dimensional connectivity in sparse VANETs, combining queuing models, percolation theory, and simulations to determine connectivity thresholds and network parameters.

Contribution

It introduces a novel method integrating queuing theory and percolation analysis to accurately evaluate connectivity in sparse vehicular networks.

Findings

Derived thresholds for vehicle arrival rates ensuring connectivity

Computed exact probabilities of street connectivity using traffic models

Validated results through numerical examples and simulations

Abstract

In this paper, we focus on two-dimensional connectivity in sparse vehicular ad hoc networks (VANETs). In this respect, we find thresholds for the arrival rates of vehicles at entrances of a block of streets such that the connectivity is guaranteed for any desired probability. To this end, we exploit a mobility model recently proposed for sparse VANETs, based on BCMP open queuing networks and solve the related traffic equations to find the traffic characteristics of each street and use the results to compute the exact probability of connectivity along these streets. Then, we use the results from percolation theory and the proposed fast algorithms for evaluation of bond percolation problem in a random graph corresponding to the block of the streets. We then find sufficiently accurate two dimensional connectivity-related parameters, such as the average number of intersections connected to each other and the size of the largest set of inter-connected intersections. We have also proposed lower bounds for the case of heterogeneous network with two transmission ranges. In the last part of the paper, we apply our method to several numerical examples and confirm our results by simulations.