Stochastic Characteristics and Simulation of the Random Waypoint Mobility Model

TL;DR

This paper investigates the stochastic stability of the discrete Random Waypoint Mobility Model used in MANET simulations, proving convergence properties and providing simulation insights to ensure long-term consistency.

Contribution

It proves that the discrete RWMM satisfies Birkhoff's ergodic theorem, ensuring convergence of time-averaged functions, and offers simulation results for better understanding.

Findings

RWMM satisfies Birkhoff's ergodic theorem

Time-averaged functions on RWMM converge

Simulation provides insights into RWMM behavior

Abstract

Simulation results for Mobile Ad-Hoc Networks (MANETs) are fundamentally governed by the underlying Mobility Model. Thus it is imperative to find whether events functionally dependent on the mobility model 'converge' to well defined functions or constants. This shall ensure the long-run consistency among simulation performed by disparate parties. This paper reviews a work on the discrete Random Waypoint Mobility Model (RWMM), addressing its long run stochastic stability. It is proved that each model in the targeted discrete class of the RWMM satisfies Birkhoff's pointwise ergodic theorem [13], and hence time averaged functions on the mobility model surely converge. We also simulate the most common and general version of the RWMM to give insight into its working.