  Information delivery using chemical molecules is an integral part of biology
at multiple distance scales and has attracted recent interest in bioengineering
and communication. The collective signal strength at the receiver (i.e., the
expected number of observed molecules inside the receiver), resulting from a
large number of transmitters at random distances (e.g., due to mobility), can
have a major impact on the reliability and efficiency of the molecular
communication system. Modeling the collective signal from multiple diffusion
sources can be computationally and analytically challenging. In this paper, we
present the first tractable analytical model for the collective signal strength
due to randomly-placed transmitters, whose positions are modelled as a
homogeneous Poisson point process in three-dimensional (3D) space. By applying
stochastic geometry, we derive analytical expressions for the expected number
of observed molecules at a fully absorbing receiver and a passive receiver. Our
results reveal that the collective signal strength at both types of receivers
increases proportionally with increasing transmitter density. The proposed
framework dramatically simplifies the analysis of large-scale molecular systems
in both communication and biological applications.
