Connectivity of Random 1-Dimensional Networks

TL;DR

This paper analyzes the probability of connectivity and coverage in 1-dimensional wireless sensor networks with sensors deployed along a line, providing formulas and estimates for minimal sensor counts based on various distance distributions.

Contribution

It introduces a method to compute connectivity and coverage probabilities for arbitrary distance distributions in 1D networks, extending prior work with new formulas and estimates.

Findings

Derived formulas for connectivity probability with arbitrary distance distributions

Provided estimates for minimal sensor numbers for key distributions

Enhanced understanding of deployment strategies in linear sensor networks

Abstract

An important problem in wireless sensor networks is to find the minimal number of randomly deployed sensors making a network connected with a given probability. In practice sensors are often deployed one by one along a trajectory of a vehicle, so it is natural to assume that arbitrary probability density functions of distances between successive sensors in a segment are given. The paper computes the probability of connectivity and coverage of 1-dimensional networks and gives estimates for a minimal number of sensors for important distributions.