Abstract
Stochastic models which are applied to model queues where the traffic intensity is greater than one and to health care models which involves huge sized populations such as human cells, viruses etc., faces the challenge of very huge number of states and hence demands huge computational cost. We studied the upper level stochastic effects in some of these models. We found that the upper level stochastic effects can’t be omitted in many situations; but can be remarkably similar to the upper level effects in a differential equation model, closely related to the stochastic model. Given a huge dimensioned stochastic model, we replaced the upper level stochastic effects with the upper level dynamics of a suitably defined differential equation model, to study certain system performance measures. This resulted in a reduction in the computational cost involved with the use of the stochastic model with a large number of states.
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Viswanath, N.C. (2019). On Combining Stochastic and Deterministic Models. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2019. Communications in Computer and Information Science, vol 1109. Springer, Cham. https://doi.org/10.1007/978-3-030-33388-1_5
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DOI: https://doi.org/10.1007/978-3-030-33388-1_5
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