Extended master equation models for molecular communication networks

Details Extended master equation models for molecular communication networks Extended master equation models for molecular communication networks

2012-04-19

arxiv.org/abs/1204.4253v2

Computer Science

Networking and Internet Architecture

Scientific paper

We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signalling molecules, which are diffused over the medium, to the receiver to realise the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time sequences specify the emission patterns of signalling molecules, while diffusion in the medium and chemical reactions at the receivers are modelled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show how RDMEX can be used to determine the mean and covariance behaviour of molecular communication networks, and derive closed-form expressions for the mean behaviour of the RDMEX model. These closed-form expressions reveal how transmitters and receivers interfere with each other in molecular communication networks. Numerical examples are provided to demonstrate the properties of the model.

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