Stochastic Modeling of Single-Hop Cluster Stability in Vehicular Ad Hoc Networks

Node clustering is a potential approach to improve the scalability of networking protocols in vehicular ad hoc networks (VANETs). High relative vehicle mobility and frequent network topology changes inflict new challenges on maintaining stable clusters. As a result, cluster stability is a crucial measure of the efficiency of clustering algorithms for VANETs. This paper presents a stochastic analysis of the vehicle mobility impact on single-hop cluster stability. A stochastic mobility model is adopted to capture the time variations of intervehicle distances (distance headways). First, we propose a discrete-time lumped Markov chain to model the time variations of a system of distance headways. Second, the first passage time analysis is used to derive probability distributions of the time periods of the invariant cluster-overlap state and cluster membership as measures of cluster stability. Third, queueing theory is utilized to model the limiting behaviors of the numbers of common and unclustered nodes between neighboring clusters. Numerical results are presented to evaluate the proposed models, which demonstrate a close agreement between analytical and simulation results.