Group joining time for Cognitive Personal Area Networks (CPANs) with independent node arrivals

The formation of a Cognitive Personal Area Network (CPAN) involves a group of nodes connecting to a dedicated coordinator. In this paper, we propose a protocol for the formation of a CPAN in which nodes arrive randomly and their times to rendezvous (TTRs) with the CPAN coordinator may overlap, partially or fully, with one another. We develop an analytical model for the group joining time, i.e., the time to form the CPAN by an arbitrary number of nodes. Experimental results show that the time to form smaller size CPANs is mostly equivalent to the sum of all nodes' joining times. As the number of nodes gets larger, the group joining time flattens, which indicates that nodes that arrive later are more likely to join the CPAN before some of the nodes that arrived earlier.