The Distance Distribution between Mobile Node and Reference Node in Regular Hexagon

TL;DR

This paper derives the distance distribution between a mobile node and reference nodes within a regular hexagon using a random waypoint model, addressing a gap in mobility-aware network analysis.

Contribution

It introduces a novel method to calculate distance distributions considering node mobility, extending static network models to dynamic scenarios.

Findings

Derived the CDF of distance between mobile and reference nodes

Validated the theoretical results with simulations

Provides a new framework for mobility-aware network analysis

Abstract

This paper presents a new method to obtain the distance distribution between the mobile node and any reference node in a regular hexagon. The existing distance distribution research mainly focuses on static network deployment and ignores node mobility. This paper studies the distribution of node distances between mobile node and any reference node. A random waypoint (RWP) migration model is adopted for mobile node. The Cumulative Distribution Function (CDF) of the distance between any reference node (inside or outside the regular hexagon) and the mobile node (inside the regular hexagon) is derived. The validity of the results is verified by simulation.