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Instruments and Systems: Monitoring, Control, and Diagnostics

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The calculation of the distribution of the output quantity GERT-network with exponential and uniformly distributed random variables
A.P. SHIBANOV, V.A. SHIBANOV

Provides an overview of applications GERT-network for modeling of industrial systems. Analysis of the characteristics of the systems
produced using equivalent transformations simplify the structure of GERT-network. The algorithms are characterized polynomial computational
complexity. The values of density distribution of continuous output value GERT-network are interpolated characteristic function
of the network. Describes how to provide the margin of error of integration of the inversion formula. The method is used if GERT-network
there are ways from input to output, including only the arc characterized by exponential and uniform distributions. The required distribution
is using the theory of residues in the presence of simple poles and removable singular points in the contour of integration. Use decomposition
of the integrand in a Laurent series in a neighborhood of infinity. An example of calculating the density distribution of the execution
time of the production process.
Keywords: GERT-network, inversion formula, residue theory, singular points, piecewise smooth closed contour.

Contacts: E-mail: mail@shibanov.ryazan.ru, E-mail: vova_shibanov@mail.ru

Pp. 01-09.

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