The multivariate models of the reserves control and their applications

The multidimensional stock control that functions in a random Markov environment is considered. The mathematical formalization of this model was considered with the use of sums of the random variables defined on the Markov chains. The authors introduce a definition of risk function of the type of downside risk measures and find the explicit formulas for its determinations. The example of the application of these formulas is provided: the tasks of the reliability and optimal configuration for the queueing problem are regarded. The formulas defining the function by the system parameters were obtained