Abstract
The spatial randomness of nanomachines and propagation time of molecules play an essential role for determining the quality of molecular communication between nanomachines. In this study, we introduce a connectivity model in which the connection between a transmit nanomachine (TN), which is randomly distributed in space, and a receive nanomachine (RN) is achieved when a molecule emitted from the TN arrives at the RN within a time constraint. In particular, this time constraint is modeled as a random lifetime to explain the dissipation phenomenon of molecules in a medium or the random arrival time of interfering molecules. Then, we characterize the local connectivity of the RN in terms of the in-degree by averaging over the spatial randomness of nanomachines and the random first passage time of molecules, which is governed by an anomalous diffusion law.
Highlights
Molecular communication is a promising paradigm to establish nanonetworks via interconnections between nanomachines for various applications in drug delivery systems, healthcare systems, nano-materials, and nano-machinery [1], [2]
The primary contributions of this paper are as follows: i) we introduce a notion of connectivity that can be established over nanonetworks with a random time constraint; ii) we analyze the local connectivity of the typical receive nanomachine (RN) on a line in terms of the in-degree; and iii) we investigate the effect of random time constraints on the connectivity along with the life expectancy of molecules to account for the dissipation phenomenon of molecules, as well as the arrival time of interfering molecules (IMs) to account for reliable connections between transmit nanomachine (TN) and the RN
We provide a closed-form expression of the in-degree of t -connectivity in a Poisson field of TNs in the sense of averaging over the spatial randomness and the random first passage time (FPT) caused by anomalous diffusion of molecules for a general analysis framework
Summary
Molecular communication is a promising paradigm to establish nanonetworks via interconnections between nanomachines for various applications in drug delivery systems, healthcare systems, nano-materials, and nano-machinery [1], [2]. Several studies have examined the concept of connectivity in a nanonetwork for molecular communication, the connectivity considering the intrinsic nature of diffusion process of molecules and the spatial randomness of nanomachines in the heterogeneous fluid medium has not been fully explored. Diffusion is characterized by the mean square displacement (MSD) of molecules, which does not increase linearly with time in anomalous diffusion [13] This extraordinary diffusion phenomenon can be observed in the crowded, heterogeneous, and complex structure environments [13]â[15]. Despite various attempts to realize molecular communication systems, anomalous diffusion channel model for the heterogeneous propagation of emitted molecules and random locations of molecules caused by the mobility of nanomachines simultaneously, has not been considered. We provide a glossary of the notations and symbols that have used in the paper in Appendix A
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