Coordination of processes according to probabilistic quality criteria with design symmetrization

The paper examines the issue of coordinating two processes by directing them towards the design values of the flow realized by these processes. The production process is considered random (since it is associated with the actions of personnel) and, in the first Markov approximation, is described by the Fokker-Planck-Kolmogorov equation. A study of the problem of optimal control of process coordination using probabilistic quality criteria shows that if one thread follows the other according to a tracking scheme, and the other provides the necessary level of readiness for the meeting, both threads will complicate each other’s management. Therefore, design symmetrization has been introduced, in which both the output of one process and the input of the second tend to the value specified by the design. Analysis of the first approximation obtained by the small decision parameter method shows that even with optimal control, the magnitude of control actions increases in proportion to the design value of the probability density and control duration; the increase in control actions over time should occur according to the cube of the exponential, that is, very slowly at the beginning of control and very sharply at the end, a similar pattern of increase is demonstrated by the dependence of control actions on the magnitude of the flow intensity, but it is expressed through hyperbolic functions.

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