Stationarity of Mobility Models Constructed with LEMMA

The Layered Mobility Model Architecture (LEMMA) stipulates that a mobility model can be divided into five distinct layers, which communicate unidirectionally via simple interlayer interfaces. It has been shown that this general framework can be used for the creation of empirical and theoretical models, and that any mobility model can be represented by the form specified by LEMMA. The fundamental result of this paper is the definition and the proof of several theorems related to the stationarity of probabilistic mobility models specified under the form defined by LEMMA. We support our findings with the help of simulation, by performing simulations with 300 different mobility models over a range of nine network setups.