Mathematical Foundations of the Layered Mobility Model Architecture - LEMMA

The layered mobility model architecture, as introduced earlier, provides a framework for the construction of microscopic mobility models for wireless network simulations. In this paper, we are continuing our study of the architecture and provide the fundamental results necessary for the definition and analysis of theoretic models. This is done for the first time for such rich mobility framework, allowing the definition of layers both based on empirical and theoretical grounds. A formal definition of a mobility model is given, applicable in a very broad range of cases. We define explicitly the mathematical entities corresponding to the different layers both for deterministic and probabilistic models. Finally, we provide the necessary proofs that any mobility model may be represented under the form specified by LEMMA.