Reflecting stochastic dynamics of active-passive crowds in a queueing theory model
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Stochastic differential equation (SDE) models have been extensively used for the description of processes with uncertainties arising in the queueing theory and behavioral sciences. 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 network models, the main focus of the present work is on the analysis of reflecting stochastic dynamics of such mixed populations. This analysis is carried out via coupled systems of SDEs in a numerical setting where we apply a kinetic Monte Carlo procedure. We provide details of the model, as well as a representative numerical example, and discuss an intrinsic interconnection between active and passive customers in the underlying stochastic process. Finally, possible extensions of the proposed methodology have been highlighted.
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