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Information delivery using chemical molecules is an integral part of biologyat multiple distance scales and has attracted recent interest in bioengineeringand communication. The collective signal strength at the receiver (i.e., theexpected number of observed molecules inside the receiver), resulting from alarge number of transmitters at random distances (e.g., due to mobility), canhave a major impact on the reliability and efficiency of the molecularcommunication system. Modeling the collective signal from multiple diffusionsources can be computationally and analytically challenging. In this paper, wepresent the first tractable analytical model for the collective signal strengthdue to randomly-placed transmitters, whose positions are modelled as ahomogeneous Poisson point process in three-dimensional (3D) space. By applyingstochastic geometry, we derive analytical expressions for the expected numberof observed molecules at a fully absorbing receiver and a passive receiver. Ourresults reveal that the collective signal strength at both types of receiversincreases proportionally with increasing transmitter density. The proposedframework dramatically simplifies the analysis of large-scale molecular systemsin both communication and biological applications.

3D Stochastic Geometry Model for Large-Scale Molecular Communication Systems