Formation of Cognitive Personal Area Networks (CPANs) Using Probabilistic Rendezvous

The formation of cognitive personal area networks (CPANs) requires a number of nodes to connect to a dedicated coordinator node. In this paper, we propose a probabilistic blind rendezvous protocol that allows nodes to concurrently rendezvous with the CPAN coordinator. This protocol allows nodes to arrive independently and their rendezvous times to overlap partially or fully with one another. We then develop a probabilistic model of the rendezvous process for both a single node and a group of nodes. The model shows that the rendezvous time, in both cases, exhibits hyperexponential behavior with large coefficient of skewness and, consequently, large variability, which may be approximated with a Gamma distribution. Furthermore, the mean group joining time tends to flatten and may even converge to a finite limit when the number of nodes is sufficiently high. However, the variability remains high due to a long tail of the distribution.