Skip to main content
Log in

Optimal Hysteresis Control for an Unreliable BMAP/SM/1 System with Two Operation Modes

  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Optimal hysteresis control strategies are designed for single-server queueing systems with waiting, batch Markov flow, semi-Markovian service, and two operation modes. Operation modes are changed not instantaneously and the failures of the server in idle states occur in a Markovian flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Neuts, M. and Lucantoni, D., Some Steady-State Distribution for the MAP=SM=1 Queue, Commun.Statistics-Stochastic Models, 1994, vol. 10, pp. 575–598.

    Google Scholar 

  2. Neuts, M., Structured Stochastic Matrices of M=G=1 Type and Their Applications, New York: Marcel Dekker, 1989.

    Google Scholar 

  3. Dudin, A.N. and Klimenok, V.I., Sistemy massovogo obsluzhivaniya s korrelirovannymi potokami (Queueing Systems with Correlated Flows), Minsk: Belarus. Gos. Univ., 2000.

    Google Scholar 

  4. Rykov, V.V., Controllable Queueing Systems, in Teoriya veroyatnostei.Matematicheskaya statistika.Teoreticheskaya kibernetika (Itogi nauki i tekhniki) (Probability Theory. Mathematical Statistics. Theoretical Cybernetics: Advances in Science and Technology), Moscow: VINITI, 1975, vol. 10, pp. 43–153.

    Google Scholar 

  5. Nobel, R.D., A Regenerative Approach to Analysis of M x =G=1 Queues with Two Service Modes, Avtom.Vychisl.Tekh., 1998, no. 1, pp. 3–14.

  6. Dudin, A.N. and Nishimura, S., Optimal Control for a BMAP=G=1 Queue with Two Service Modes, Math.Probl.Eng., 1999, vol. 5, no. 3, pp. 397–420.

    Google Scholar 

  7. Dudin, A.N. and Nishimura, S., Optimal Hysteretic Control for a BMAP=SM=1=N Queue with Two Service Modes, Math.Probl.Eng., 2000, vol. 5, no. 5, pp. 255–273.

    Google Scholar 

  8. Lucantoni, D.M. New Results on the Single-Server Queue with a Batch Markovian Arrival Process, Commun.Statistics-Stochastic Models, 1991, vol. 7, no. 1, pp. 1–46.

    Google Scholar 

  9. Lu, F.V. and Serfozo, R.F., M=M=1 Queueing Decision Process with Monotone Hysteretic Optimal Policies, Oper.Res., 1984, vol. 32, pp. 1116–1129.

    Google Scholar 

  10. Rykov, V.V., Hysteresis in Controlled Queueing Systems, Vest.Ross.Univ.Druzhby Narodov, 1995, vol. 3, pp. 101–111.

    Google Scholar 

  11. Dudin, A.N. and Klimenok, V.I., Multidimensional Quasi-Toeplitz Markov Chains, J.Appl.Math.Stoch.Anal., 1999, vol. 12, no. 4, pp. 393–415.

    Google Scholar 

  12. Graham, A., Kronecker Products and Matrix Calculus with Aplications, Chichester: Ellis Horwood, 1981.

    Google Scholar 

  13. Bocharov, P.P. and Pechinkin, A.V., Teoriya massovogo obsluzhivaniya (Queueing Theory), Moscow: Ross. Univ. Druzhby Narodov, 1995.

    Google Scholar 

  14. Klimov, G.P., Stokhasticheskie sistemy obsluzhivaniya (Stochastic Queueing Systems), Moscow: Nauka, 1966.

    Google Scholar 

  15. Gail, H.R., Hantler, S.L., Sidi, M., and Taylor, B.A., Linear Independence of Root Equations for M=G=1 Type of Markov Chains, Queueing Syst., 1995, vol. 20, pp. 321–329.

    Google Scholar 

  16. Gail, H.R., Hantler, S.L., and Taylor, B.A., Spectral Analysis of M=G=1 and GI=M=1 Type Markov Chains, Adv.Appl.Prob., 1996, vol. 28, pp. 114–165.

    Google Scholar 

  17. Dudin, A.N., Optimal Control for a M x =G=1 Queue with Two Operation Modes, Prob.Eng.Inf.Sci., 1997, vol. 11, pp. 255–265.

    Google Scholar 

  18. Dudin, A.N., Optimal Multithreshold Control for a BMAP=G=1 Queue with N Service Modes, Queueing Syst., 1998, vol. 30, no. 3–4, pp. 273–287.

    Google Scholar 

  19. Skorokhod, A.V., Teoriya veroyatnostei i sluchainykh protsessov (Theory of Probability and Random Processes), Kiev: Vishcha Shkola, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dudin, A.N. Optimal Hysteresis Control for an Unreliable BMAP/SM/1 System with Two Operation Modes. Automation and Remote Control 63, 1585–1596 (2002). https://doi.org/10.1023/A:1020496612713

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020496612713

Keywords

Navigation