On Clustering Phenomenon in Mobile Partitioned Networks
According to different kinds of connectivity, we can distinguish three types of mobile ad-hoc networks: dense, sparse and clustered networks. This paper is about modeling mobility in clustered networks, where nodes are concentrated into clusters of dense connectivity, and in between there exists sparse connectivity. The dense and sparse networks are extensively studied and modeled, but not much attention is paid to the clustered networks. In the sparse and clustered networks, an inherently important aspect is the mobility model, both for the design and evaluation of routing protocols. We propose a new mobility model for clustered networks, called Heterogeneous Random Walk. This model is simple, mathematically tractable and most importantly it captures the phenomenon of emerging clusters, observed in real partitioned networks, in an elegant way. We provide a closed-form expression for the stationary distribution of node position and we give a recipe for the "perfect simulation". Moreover, based on the real mobility trace we provide strong evidence for the main macroscopic characteristics of clustered networks captured by the proposed mobility model. For the very first time in the literature we show evidence for the correlation between the spatial speed distribution and the cluster formation. We also present the results of the analysis of real cluster dynamics caused by nodes' mobility.