Automation and Remote Control

, Volume 75, Issue 3, pp 422–446 | Cite as

Control and observation for dynamical queueing networks. I

Stochastic Systems, Queueing Systems


For the optimal control problem for a queueing network state, we write the Bellman equation and give examples of its analytic and numerical solutions. In the first part, we give examples of solving optimal control problems for elementary network structures. In the second part, we give a solution of the optimal control problem for the network state and observations that gives an answer to the question of what, when, where, and how to measure in the network while solving dynamic routing problems. We give examples of solving synthesis problems for optimal controls and optimal network informational structures for modern telecommunicational systems.


Remote Control Optimal Control Problem Queue Length Time Moment Busy Period 
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  1. 1.
    Solodyannikov, Yu.V., Some Problems of Network Measurement, in Teoreticheskie problemy vychislitel’nykh setei. Nauchn. Sovet po kompleksnoi probleme “Kibernetika” Akad. Nauk SSSR (Theoretical Problems of Computational Networks, Research Council on the Complex Problem “Cybernetics” of Acad. Sci. USSR), Kuibyshev: Kuibysh. Gos. Univ., 1986, pp. 74–102.Google Scholar
  2. 2.
    Solodyannikov, Yu.V., On Statistics of Queueing Systems and Networks, in Problemy ustoichivosti stokhasticheskikh modelei. Tr. X Vses. seminara (Stability Problems in Stochastic Models, Proc. X All-Union Seminar), Kuibyshev: Kuibysh. Gos. Univ., 1987, pp. 101–116.Google Scholar
  3. 3.
    Dynkin, E.B. and Yushkevich, A.A., Upravlyaemye markovskie protsessy i ikh prilozheniya (Controllable Markov Processes and Their Applications), Moscow: Nauka, 1975.MATHGoogle Scholar
  4. 4.
    Sennott, L.I., Stochastic Dynamic Programming and the Control of Queueing Systems, New York: Wiley-Interscience, 1999.MATHGoogle Scholar
  5. 5.
    Rykov, V.V., Controllable Queueing Systems, Itogi Nauki Tekhn., Ser. Teor. Veroyat. Mat. Stat. Teor. Kibern., Moscow: VINITI, 1975, no. 12, pp. 43–153.Google Scholar
  6. 6.
    Ceci, C., Gerardi, A., and Tardelli, P., Existence of Optimal Controls for Partially Observed Jump Processes, Acta Appl. Math., 2002, vol. 74, pp. 155–175.CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Eliott, R.J., Aggoun, L., and Moore, J.B., Hidden Markov Models: Estimation and Control, New York: Springer, 2008.Google Scholar
  8. 8.
    Miller, A., Dynamic Control of Access with Active Users, Inform. Proc., 2009, vol. 9, no. 1, pp. 1–17.Google Scholar
  9. 9.
    Miller, B.M., Miller, G.B., and Semenikhin, K.V., Methods to Design Optimal Control of Markov Process with Finite State Set in the Presence of Constraints, Autom. Remote Control, 2011, vol. 72, no. 2, pp. 323–341.CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Kleinrock, L., Queueing Systems, New York: Wiley, 1976. Translated under the title Teoriya massovogo obsluzhivaniya, Moscow: Mashinostroenie, 1979.MATHGoogle Scholar
  11. 11.
    Boel, R. and Varaia, P., Optimal Control of Jump Processes, SIAM J. Control Optim., 1977, vol. 15, no. 1, pp. 92–119.CrossRefMATHGoogle Scholar
  12. 12.
    Kleinrock, L., Queueing Systems, vol. I: Theory, New York: Wiley-Interscience, 1975. Translated under the title Vychislitel’nye sistemy s ocheredyami, Moscow: Mir, 1979.Google Scholar
  13. 13.
    Baccelli, F. and Massey, W.A., A Transient Analysis of the Two-Node Jacson Network, INRIA Rapport de Recherche, 1988, no. 852, pp. 1–11.Google Scholar
  14. 14.
    Massey, W.A., Calculating Exit Times for Series Jacson Networks, J. Appl. Prob., 1987, vol. 24, no. 1, pp. 226–234.CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Miller, A.B., Using Methods of Stochastic Control to Prevent Overloads in Data Transmission Networks, Autom. Remote Control, 2010, vol. 71, no. 9, pp. 1804–1815.CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Klimov, G.P., Stokhasticheskie sistemy obsluzhivaniya (Stochastic Queueing Systems), Moscow: Nauka, 1966.Google Scholar
  17. 17.
    Ivchenko, G.I., Kashtanov, V.A., and Kovalenko, I.N., Teoriya massovogo obsluzhivaniya (Queueing Theory), Moscow: Vysshaya Shkola, 1982.MATHGoogle Scholar
  18. 18.
    Matveev, V.F. and Ushakov, V.G., Sistemy massovogo obsluzhivaniya (Queueing Systems), Moscow: Mosk. Gos. Univ., 1984.MATHGoogle Scholar

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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.SJC “Samara-Dialog”SamaraRussia

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