Realistic Boundary Conditions for Ad Hoc Network Node Mobility Models and a New Approach to the Random Waypoint Model

TL;DR

This paper analyzes border effects in mobility models for ad hoc networks, demonstrating conditions for diffusion equation compliance, and proposes a generalized RWP model for more uniform node distributions.

Contribution

It identifies conditions for mobility models to obey the diffusion equation and introduces a generalized RWP model that avoids border effects and achieves uniform distributions.

Findings

RD model satisfies diffusion conditions

New volume rule reproduces RWP behavior

Proposed model improves uniformity of node distribution

Abstract

In this paper, we examine the cause of the border effect observed in many mobility models used to construct simulations of ad hoc networking protocol performance. We specify conditions under which a node mobility model must produce spatial mobile node distribution functions that obey the diffusion equation. In particular demonstrate that these conditions are satisfied by the random direction (RD) model. We show that it is possible to construct mobility models that attain uniform steady-state distributions without resorting to reflection or ``wrapping'' of nodes at the border of a test region. Finally, we show that the random waypoint (RWP) model may be reproduced by the application of a ``volume rule'' to an RD model. This volume rule violates the assumptions that lead to the diffusion equation. We suggest a generalization of the RWP model that can provide more uniform mobile node distributions.