Reflecting stochastic dynamics of active-passive populations with applications in operations research and neuroscience

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.