A.P. Shibanov – Dr.Sc.(Eng.), Professor, Department of Computer-Aided Design Systems, Ryazan State Radio Engineering University
V.A. Shibanov – Ph.D.(Eng.), Associate Professor, Department of Computer-Aided Design Systems, Ryazan State Radio Engineering University
GERT-networks (GERT: Graphical Evaluation and Review Technique), proposed by Alan Pritzker, are widely used to study the proba-bilistic behavior of technical and social systems. They were used to solve modeling problems: industrial complexes; local networks and data transmission networks; stochastic behavior of programs; queuing and optimization processes; characteristics of technical systems with blocks of cold reserve, etc.
In the GERT-network, for any path, the condition of additivity of random variables characterizing arcs is fulfilled. Additivity is a property of quantities with respect to addition, consisting in the fact that the value of the value corresponding to the whole object is equal to the sum of the values of the quantities corresponding to its parts. In GERT-networks such quantities are, for example, time, cost, volumes of RAM (without reusability), and so on.
In this paper we consider GERT-networks with the properties of quantities with respect to both the addition operation and the subtraction operation.
The GERT Explorer program was developed and used to get results.
By negative random variables we mean those quantities, the realization of which must be subtracted from the result accumulated at a given node by performing operations preceding this one. To specify negative random variables, the properties of the characteristic functions are used. Expansion of the probability density corresponds to the contraction of its characteristic function. Each negative random variable is associated with some positive random variable, relative to which the subtraction and compression function is per-formed in k times and, correspondingly, the scaling of the characteristic function of the latter.
An example of the process of primary processing of telemetric information is considered when performing: 1) rejecting anomalously inaccurate measurements, 2) eliminating redundancy by eliminating unnecessary information.
If the operations of primary processing are stochastic, we can predict the amount of memory needed to store data on the secondary processing.
Positive random variables reflect the receipt of the original telemetric information. Negative random variables are used to model the process of eliminating anomalous values and compressing information during primary processing. As a result, probabilistic estimates of the reduction in the volume of the telemetry after the initial processing are calculated.
In this example, only two negative random variables were used. In GERT-network such operations can be performed on any trajectory from the source node to the node-drain. As a result, all operations of the GERT network can be divided into two subsets: a subset of arcs associated with positive random variables, and a subset of arcs associated with negative random variables. Thus, the GERT network can be divided into two parts, which are composed only of positive and only negative random variables. On each trajectory, the arcs of one subset are selected. The divided GERT network reflects, in the general case, the joint process of increasing a certain number (useful process execution time, memory costs and other additive random variables) reflected by some variable and the loss of this quantity. In the example above, this is the amount of data excluded from the source array during the initial processing phase.
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- Koryachko V.P., Fam X.L., Shibanov A.P. Kanal peredachi danny’x s otkazami i vosstanovleniem rabotosposobnosti // Vestnik RGRTU. 2016. № 4(58) S. 37−41.