Nature inspired node density estimation for molecular nanonetworks

The problem of estimating the node density in ad hoc networks is a significant one for protocol design. In molecular nanonetworks, the node density estimation problem poses additional challenges due to the limited processing and communication capabilities of the network nodes which necessitate the design of simple to implement distributed solutions, and the diffusion based communication channel which is different from traditional electromagnetic networks. In this work, inspired by the quorum sensing process, we propose and analyze a new node density estimation scheme based on synchronous transmission of all network nodes and measurement of the received molecular concentration. We show that when the synchronous transmission is performed in infinite space, a linear parametric model of the node density can be derived which can be used for estimation purposes. When, however, the transmission is performed over a finite space the model becomes time varying. To overcome the difficulties associated with the time varying nature we propose the use of periodic transmission which for large enough values of the period transforms the linear model into a static one. An online parameter identification technique is then introduced to estimate the node density using the derived linear static parametric models. The utilization of the node density estimates to adaptively regulate probabilistic flooding in network structures relevant to nanonetworks is then considered. The random geometric graph model and uniform grid structures are used to demonstrate how the node estimates can be used to dictate the desired rebroadcast probabilities, through analysis and simulations.