Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Determination of stochastic characteristics of primary treatment of telemetrated parameters with the use of GERT networks with negative random values


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.

  1. Pritsker A.A. GERT. Graphical evaluation and review technique. Memorandum RM-4973-NASA. 1966. 138 p.
  2. Fillips D., Garsia Dias A. Metody’ analiza setej. M.: Mir. 1984. 496 c.
  3. Abdullaev D.A., Amirsaidov U.B. Modelirovanie lokal’ny’x vy’chislitel’ny’x setej s uchetom veroyatnostno-vremenny’x xarakteristik // Avtomatika i telemexanika. 1994. № 3. S. 151−160.
  4. Zaxarov G.P. Metody’ issledovaniya setej peredachi danny’x. M.: Radio i svyaz’. 1982. 208 s.
  5. Shibanov A.P. A Software Implementation Technique for Simulation of Ethernet Local Erea Networks // Programming and Computing Software. Plenum Press New York, NY, USA. November-December 2002. V. 28. № 6. P. 349−355.
  6. Koryachko V.P., Shibanov A.P., Kravchuk N.V., Shibanov V.A. Metod rasstanovki kontrol’ny’x tochek v programmax mikrokontrollerov so storozhevy’mi tajmerami // Pribory’ i sistemy’. Upravlenie, kontrol’, diagnostika. 2008. № 11. S. 44−49.
  7. Wang J., Chen M. Remanufacturing process for used automotive electronic control components in China // Journal of Remanufacturing. 2013. № 3. P. 42−47.
  8. Razeghi S., Iranzadeh S., Youshanloi K.R., Bagherpour M., Bevrani H. Simplifying probable combined network through using GERT method // Reef Resources Assessment and Management Technical Paper. 2014. V. 43. P. 73−81.
  9. Wyrozebski P., Wyrozebska A. Challenges of project planning in the probabilistic approach using PERT, GERT and Monte Carlo // Journal of Management and Marketing. 2013. V. 1. № 1. P. 1−7.
  10. Agarwal M., Pooja Mohan P. Reliability Analysis of Consecutive k, r Out-Of n: DFM System using GERT // International Journal of Operations Research. 2007. V. 4. № 2. P. 110−117.
  11. Feili H., Alavi S.H., Najmoddin M. Optimization and organization of human forces in a center of customers’ affairs by help of simulation and GERT networks // Kuwait Chapter of Arabian Journal of Business and Management Review. 2014. V. 3. № 12a. P. 261−271.
  12. Antkiewicz R., Dyk M., Kasprzyk R., Najgebauer A., Pierzchalam D., Tarapata Z. Criminal procedure management based on BPM simulation // Information Systems in Management. 2013. V. 2 (2). P. 87−99.
  13. Jose. K.P. GERT Analysis of a Three Unit Cold Standby System with Single Repair Facility // Journal of Computer and Mathematical Sciences. 2012. V. 3. № 1. P. 1−130.
  14. Hashemin S.S., Fatemi Ghomi T.F. Constrained consumable resource allocation in alternative stochastic networks via multi-objective decision making // Journal of Industrial Engineering International. 2012. V. 8. P. 1−9.
  15. Hashemin S.S. Fuzzy completion time for alternative stochastic networks // J. Ind. Eng. Spring. 2010. V. 6 (11). P. 17−22.
  16. Shibanov A.P. Finding the distribution density of the time taken to fulfill the GERT network on the basis of equivalent simplifying transformations // Automation and Remote Control. 2003. T. 64. № 2. S. 279−287.
  17. Shibanov A.P. Metod e’kvivalentny’x uproshhayushhix preobrazovanij GERT-setej i ego prilozheniya // Vestnik RGRTU. 2012. № 39−2. S. 76−83.
  18. Izhvanov Yu.L., Koryachko V.P., Shibanov A.P., Sapry’kin A.N., Luk’yanov O.V. Optimizacziya setej s dozirovannoj balansirovkoj nagruzki i piringovy’mi kanalami // Vestnik RGRTU. 2013. № 1(43). S. 67−74.
  19. Koryachko V.P., Luk’yanov O.V., Shibanov A.P. Naxozhdenie skry’togo parallelizma protokolov dlya uluchsheniya xarakteristik seti peredachi danny’x poligonnogo izmeritel’nogo kompleksa // Vestnik RGRTU. 2014. № 47. S. 68−75.
  20. 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.
June 24, 2020
May 29, 2020

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio