A Mean Field Based Methodology for Modeling Mobility in Ad Hoc Networks

In this paper we propose a methodology for the modeling and analysis of ad hoc networks composed by a large number of nodes moving among geographical regions. This methodology uses compositional construction of stochastic Petri nets (SPN) for building the model which allows for specifying the model and the required performance indices at a high level of abstraction. As our aim is to consider real scenarios with several geographical regions and non-trivial user behavior in each region, the size of the state space of the model can easily grow too large to analyze with exact analytical approaches or even with simulation. For this reason, we propose to carry out the analysis by constructing the mean field approximation of the behavior of the SPN. The approximation is provided by a set of ordinary differential equations (ODE) that can be derived automatically from the SPN and can be solved numerically with low computational effort even for large models. The methodology is illustrated on a case study, modeling application spreading in a mobile environment. It will be shown that the approximate results obtained by the mean field approach capture well the behavior of the system.