Automation and Remote Control

, Volume 80, Issue 9, pp 1694–1703 | Cite as

The Degree of Parallelism in Generalized Stochastic Network

  • N. N. IvanovEmail author
Large Scale Systems Control


For the generalized stochastic network the concept of degree of parallelism is entered. The method of determination of this value is offered. It makes the choice of the minimum number of performers of the network at which there is no formation of queues for passing of arcs.


generalized stochastic network path the distribution of arcs duration the Bron–Kerbosch algorithm 


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  1. 1.
    Golenko-Ginzburg, D.I., Stokhasticheskie setevye modeli planirovaniya i upravleniya razrabotkami (Stochastic Network Models in R&D Projecting), Voronezh: Nauchnaya Mysl’, 2010.Google Scholar
  2. 2.
    Eliseev, V.V. and Ignatushchenko, V.V., The Issue of Reliable Execution of Complex Sets of Problems in Control Parallel Computing Systems, Probl. Upravlen., 2006, no. 6, pp. 6–18.Google Scholar
  3. 3.
    Ermakov, S.M. and Mikhailov, G.A., Statisticheskoe modelirovanie (Statistical Modeling), Moscow: Nauka, 1982.Google Scholar
  4. 4.
    Ivanov, N.N., Ignatushchenko, V.V., and Mikhailov, A.Yu., Static Forecasting of the Execution Times of Complexes of Interrelated Jobs in the Multiprocessor Computer Systems, Autom. Remote Control, 2005, no. 6, pp. 931–943.Google Scholar
  5. 5.
    Ivanov, N.N., Ignatushchenko, V.V., and Mikhailov, A.Yu., Calculation of Estimates of the Distribution of Execution Time of Complexes of Interrelated Works in Multiprocessor Computing Systems, in Trudy Instituta (Institute Proceedings), Moscow: Inst. Probl. Upravlen., 2006, vol. XXVII, pp. 124–135.Google Scholar
  6. 6.
    Ivanov, N.N., Analytical and Simulation Models of Generalized Stochastic Networks, Upravlen. Bol’sh. Sist., 2015, no. 53, pp. 27–44.Google Scholar
  7. 7.
    Ivanov, N.N., Redundancy in Parallel Computing Systems that Perform Complexes of InterrelatedWork, Proc. 6th Int. Conf. on Parallel Computing and Control Problems (PACO’2012), Moscow: Inst. Probl. Upravlen., 2012, vol. 1, pp. 134–139.Google Scholar
  8. 8.
    Ivanov, N.N., Optimal Redundancy in Parallel Computing Systems Performing Interconnected Work Complexes, Proc, XII All-Russian Conf. on Control Problems, Moscow: Inst. Probl. Upravlen., 2014, pp. 7246–7255.Google Scholar
  9. 9.
    Ivanov, N.N. and Shastun, V.V., Determination of Exact Upper Estimates of Time Taken to Perform Complex Sets of Problems in Control, Parallel Computing Systems, Autom. Remote Control, 2010, vol. 71, no. 9, pp. 1899–1908.CrossRefzbMATHGoogle Scholar
  10. 10.
    Ignatushchenko, V.V. and Isaeva, N.A., Redundantization of Interdependent Program Modules for Parallel Control Computing Systems: Organization, Estimation of Fault-tolerance, Formalized Description, Autom. Remote Control, 2008, no. 10, pp. 1778–1795.Google Scholar
  11. 11.
    Harary, F., Graph Theory, London: Addison Wesley, 1969. Translated under the title Teoriya grafov, Moscow: Mir, 1973.CrossRefzbMATHGoogle Scholar
  12. 12.
    Bron, C. and Kerbosch, J., Algorithm 457: Finding all Cliques of an Undirected Graph, Commun. ACM, 1973, vol. 16, pp. 575–577.CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesMoscowRussia

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