Some control problems for non-homogeneous birth-death processes
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2016.3.09Keywords:
control problem, stabilization problem, non-homogeneous Markov birth-death process, birth intensity, death intensity, moment of extinctionAbstract
We consider non-homogeneous Markov birth-death processes in a case of the constant ratio c of death and birth intensities. We solve three control problems by choosing the parameter c for such processes. We solve the problem of minimizing the probability of moving out of range as t→∞. We use the golden section search to find the existing minima, which depend on a threshold value and an integral birth intensity value. We solve the control problem by choosing the parameter c using the stabilization function. The existence of a minimum is proved and the minimum is found; also, important selected cases are considered. The parameter identification problem for an exponential stabilization function is also solved. We solve the problem of minimizing the mean of an extinction time with a small probability of exceeding the threshold. The convergence conditions for the mean are found, the conditions of the threshold exceeding probability are simplified, the problem is solved under an assumption of a constant birth intensity.References
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