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Analysis and Optimization of a Controlled Model for a Closed Queueing Network

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Abstract

We consider a closed network consisting of two queuing systems: the main system simulates a packet transmission queue over an unreliable communication channel, and the auxiliary multiserver system contains lost packets for resending. The service rate in the main system is controllable and is supposed to be optimized with the aim of minimizing the time of successful transmission, taking into account the cost of using network resources. We obtain optimality conditions in two cases: 1) in the model based on fluid approximation in the presence of heavy load; 2) in the steady state using stationary strategies.

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References

  1. Miller, B.M., Avrachenkov, K.E., Stepanyan, K.V., and Miller, G.B., Flow Control as a Stochastic Optimal Control Problem with Incomplete Information, Probl. Inform. Transm., 2005, vol. 41, no. 2, pp. 150–170.

    Article  Google Scholar 

  2. Miller, B.M., Optimization of Queuing System via Stochastic Control, Automatica, 2009, vol. 45, pp. 1423–1430.

    Article  MathSciNet  Google Scholar 

  3. Rieder, U. and Winter, J., Optimal Control of Markovian Jump Processes with Partial Information and Applications to a Parallel Queueing Model, Math. Meth. Oper. Res., 2009, vol. 70, pp. 567–596.

    Article  MathSciNet  Google Scholar 

  4. Solodyannikov, Yu.V., Control and Observation for Dynamical Queueing Networks. I, Autom. Remote Control, 2014, vol. 75, no. 3, pp. 422–446.

    Article  MathSciNet  Google Scholar 

  5. Solodyannikov, Yu.V., Control and Observation for Dynamical Queueing Networks. II, Autom. Remote Control, 2014, vol. 75, no. 5, pp. 880–899.

    Article  MathSciNet  Google Scholar 

  6. Kuznetsov, N.A., Myasnikov, D.V., and Semenikhin, K.V., Optimization of Two-Phase Queuing System and Its Application to the Control of Data Transmission Between Two Robotic Agents, J. Commun. Technol. Electron., 2017, vol. 62, no. 12, pp. 1484–1498.

    Article  Google Scholar 

  7. Borisov, A.V., Miller, G.B., and Stefanovich, A.I., Controllable Markov Jump Processes. I. Optimum Filtering Based on Complex Observations, J. Comput. Syst. Sci. Int., 2018, vol. 57, no. 6, pp. 890–906.

    Article  Google Scholar 

  8. Borisov, A.V., Miller, G.B., and Stefanovich, A.I., Controllable Markov Jump Processes. II. Monitoring and Optimization of TCP Connections, J. Comput. Syst. Sci. Int., 2019, vol. 58, no. 1, pp. 12–28.

    Article  Google Scholar 

  9. Kogan, A.Ya., Liptser, R.Sh., and Smorodinskii, A.V., Gaussian Diffusion Approximation of Closed Markov Models of Computer Networks, Probl. Inform. Transm., 1986, vol. 22, no. 1, pp. 38–51.

    MATH  Google Scholar 

  10. Gordon, W.J. and Newell, F.G., Closed Queuing Systems with Exponential Servers, Oper. Res., 1967, vol. 15, no. 2, pp. 254–265.

    Article  Google Scholar 

  11. Kel’bert, M.Ya. and Sukhov, Yu.M., Mathematical Problems in Queueing Network Theory, in Itogi Nauki Tekh., Teor. Veroyat. Mat. Statist. Teor. Kibern., Moscow: VINITI, 1988, vol. 26, pp. 3–96.

    Google Scholar 

  12. Kitaev, M.Y. and Rykov, V.V., Controlled Queueing Systems, Boca Raton: CRC, 1995.

    MATH  Google Scholar 

  13. Sennott, L.I., Stochastic Dynamic Programming and the Control of Queueing Systems, New York: Wiley, 1999.

    MATH  Google Scholar 

  14. Whitt, W., Stochastic-Process Limits. An Introduction to Stochastic-Process Limits and Their Application to Queues, New York: Springer, 2002.

    Book  Google Scholar 

  15. Anisimov, V.V., Switching Processes in Queueing Models, Hoboken: Wiley, 2008.

    Book  Google Scholar 

  16. Stidham, S., Optimal Design of Queueing Systems, New York: Chapman & Hall/CRC, 2009.

    Book  Google Scholar 

  17. Altman, E., Constrained Markov Decision Processes, Boca Raton: Chapman & Hall/CRC, 1999.

    MATH  Google Scholar 

  18. 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.

    Article  MathSciNet  Google Scholar 

  19. Schechner, Z. and Yao, D., Decentralized Control of Service Rates in a Closed Jackson Network, IEEE Trans. Automat. Control, 1989, vol. 34, no. 2, pp. 236–240.

    Article  MathSciNet  Google Scholar 

  20. Ma, D.-J. and Cao, X.-R., A Direct Approach to Decentralized Control of Service Rates in a Closed Jackson Network, IEEE Trans. Automat. Control, 1994, vol. 39, no. 7, pp. 1460–1463.

    Article  MathSciNet  Google Scholar 

  21. Stepanov, S.N. and Stepanov, M.S., Construction and Analysis of a Generalized Contact Center Model, Autom. Remote Control, 2014, vol. 75, no. 11, pp. 1936–1947.

    Article  MathSciNet  Google Scholar 

  22. Liptser, R.S. and Shiryayev, A.N., Statistics of Random Processes, New York: Springer, 2005, 3rd ed.

    MATH  Google Scholar 

  23. Fleming, W.H. and Rishel, R.W. Deterministic and Stochastic Optimal Control, New York: Springer-Verlag (1975).

    Book  Google Scholar 

  24. Fleming, W.H. and Rishel, R.W. Translated under the title Optimal’noe upravlenie determinirovannymi i stokhasticheskimi sistemami, Moscow: Mir, 1978.

    Google Scholar 

  25. Ioffe, A.D. and Tikhomirov, V.M., Teoriya ekstremal’nykh zadach (Theory of Extremal Problems) Moscow: Nauka, 1974.

    Google Scholar 

  26. Aubin, J.P. and Ekeland, I., Applied Nonlinear Analysis, New York: Wilwy, 1984.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Kotelnikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow, Russia

    N. A. Kuznetsov & K. V. Semenikhin

  2. Moscow Institute of Physics and Technology, Moscow, Russia

    N. A. Kuznetsov

  3. Moscow Aviation Institute, Moscow, Russia

    K. V. Semenikhin

Authors
  1. N. A. Kuznetsov
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  2. K. V. Semenikhin
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Corresponding authors

Correspondence to N. A. Kuznetsov or K. V. Semenikhin.

Additional information

This paper was recommended for publication by E. Ya. Rubinovich, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 3, pp. 67–85.

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Kuznetsov, N.A., Semenikhin, K.V. Analysis and Optimization of a Controlled Model for a Closed Queueing Network. Autom Remote Control 81, 430–444 (2020). https://doi.org/10.1134/S0005117920030042

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  • DOI: https://doi.org/10.1134/S0005117920030042

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