Spatial Stationarity of Link Statistics in Mobile Ad Hoc Network Modelling

The performance evaluation of ad hoc network components through simulation allows for isolation of parameters, easy access to global quantities and a statistically significant number of repeatable trials. In designing network protocols, it is important to investigate the relationship between global network performance and the underlying locally observed network characteristics. Mobility models are used to define the movement of nodes in the simulation space. A wide variety of mobility models exist, and the choice of mobility model has significant influence over locally observed metrics. Unfortunately, many mobility models exhibit spatial and temporal non-stationarity of important metrics, such that global averages of certain metrics are not representative of local observations. This finding impacts on the development of adaptive ad hoc architectures. This paper explores the spatial stationarity of frequently used mobility models. It focuses on the importance of stationarity in relation to the evaluation of performance studies. The spatial non-stationarity of link statistics, and the impact of this artefact on network performance evaluation is examined for the Toroidal Random Waypoint and Random Direction mobility models. We show that the Toroidal Random Waypoint model exhibits spatial stationarity of link statistics. Furthermore, we demonstrate that network performance studies in spatially stationary environments produce dissimilar results to those produced by non-stationary environments. This shows the importance of spatial stationarity when investigating global network performance and locally observed network characteristics.