Exponential random geometric graph process models for mobile wireless networks

In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential first order autoregressive (AR(1)) process. The transition probability matrix and stationary distribution are derived for the Markov chains in terms of network connectivity and the number of components. We characterize an algorithm for the hitting time regarding disconnectivity. In addition, we also study static topological properties including connectivity, degree distributions and the largest nearest neighbor distance associated with the random graph process. Both closed form results and limit theorems are provided.