Characterizing the Probability of Collision Between Information Particles in Molecular Communications

Abstract

Most of the works reported in the existing molecular communication literature make an assumption that the information molecules released in the fluid medium do not interact with each other and follow independent and identically distributed paths to the receiver. However, there are certain molecular transport paradigms where such an assumption does not hold and the interactions between the information molecules play an important role in characterizing such molecular communication processes. Motivated by this, we provide in this letter an analysis for the possible interaction between two information molecules that are released into the fluid medium a certain time interval apart in the case of a molecular timing channel. We calculate the probability that the two information molecules collide before any one of them is absorbed at the boundary. We also derive the distribution of the collision time and the collision position of the information molecules. Furthermore, numerical results corroborate our analysis.