Distributing Nanomachines for Minimizing Mean Residence Time of Molecular Signals in Bionanosensor Networks

In this paper, we consider a bionanosensor network composed of nano-to-micro-scale nanomachines distributed over a 1- or 2-D bounded area. The goal of the bionanosensor network is to detect and remove a target signal that appears in the monitoring area and propagates via Brownian motion. The problem considered in this paper is formulated as a nanomachine placement problem to minimize the mean residence time of the target signals, this being defined as the average amount of time that a target signal spends in the monitoring area. We first formulate the nanomachine placement problem, and then design three simple biologically implementable approaches and one heuristic approach for the placement of nanomachines, respectively, called random, proportional, regular, and greedy placements. In the random placement, nanomachines are distributed randomly over the monitoring area. In the proportional placement, more nanomachines are distributed over the monitoring area where the target signals appear more frequently. In the regular placement, nanomachines are distributed to maintain a specific distance from adjacent nanomachines. In the greedy placement, nanomachines are optimally placed one by one. We evaluate the four approaches through simulation in terms of the mean residence time under various scenarios. We also analyze the mean residence time under a simplified setting with respect to the size of the area and number of nanomachines to be placed.