Counting Geodesic Paths in 1D VANETs

TL;DR

This paper analytically derives the mean and variance of the number of shortest multihop paths (geodesics) in 1D vehicular ad hoc networks, which is crucial for improving communication efficiency and security.

Contribution

It provides the first analytical calculation of the mean and variance of geodesic counts in 1D VANETs, advancing understanding of network path statistics.

Findings

Derived the mean number of geodesics in 1D VANETs

Calculated the variance of geodesic counts

Provides foundational statistics for VANET performance analysis

Abstract

In the IEEE 802.11p standard addressing vehicular communications, Basic Safety Messages (BSMs) can be bundled together and relayed as to increase the effective communication range of transmitting vehicles. This process forms a vehicular ad hoc network (VANET) for the dissemination of safety information. The number of "shortest multihop paths" (or geodesics) connecting two network nodes is an important statistic which can be used to enhance throughput, validate threat events, protect against collusion attacks, infer location information, and also limit redundant broadcasts thus reducing interference. To this end, we analytically calculate for the first time the mean and variance of the number of geodesics in 1D VANETs.