Strong Stochastic Stability for MANET Mobility Models

Abstract

At the core of any MANET simulation is a mobility model. To help ensure reliable simulation results, it is of interest to know if the mobility model is stable: Will time-averaged measurements of "mobility model events" converge? For example, does the time-averaged distance between a pair of nodes converge as simulation time increases? In this paper, we study the stability of a class of discrete Random Waypolnt Mobility Models (RWMMs). This class includes the classic Random Waypolnt Mobility Model. We show that each mobility model in this class satisfies a pointwise ergodic theorem (a generalized strong law of large numbers); thus, all bounded time-averaged measurements of mobility model events converge with probability one. A corollary of this ergodic theorem shows that each mobility model in this class also possesses a time-stationary regime.