  Stochastic dynamic models have been extensively used for the description of
processes with uncertainties arising in the operations research, behavioral
sciences, and many other application areas. A large class of the problems from
these domains is characterized by the necessity to deal with several distinct
groups of populations, which are usually labeled as "active" and "passive".
Motivated by important applications of queueing networks and neuroscience, the
main focus of the present work is on the analysis of reflecting stochastic
dynamics of such mixed populations. We develop a general mathematical modeling
framework to describe the reflecting stochastic dynamics for active-passive
populations. The analysis of this model is carried out via a combination of
low- and high-delity results obtained from the solution of the underlying
coupled system of SDEs and from the simulations with a
statistical-mechanics-based lattice gas model, where we employ a kinetic Monte
Carlo procedure. We provide details of the queueing theory and neuronal models
and discuss a relationship between reflecting SDEs and a model of queueing
theory via a limit theorem. Furthermore, we present several representative
numerical examples, and discuss an intrinsic interconnection between active and
passive particles in the underlying stochastic process. Finally, possible
extensions of the proposed methodology have been highlighted.
