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Optimal Allocation Problem in the Machine Repairman System with Heterogeneous Servers

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Information Technologies and Mathematical Modelling (ITMM 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 487))

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Abstract

A controllable repairman model consists of L machines subject to failures and two repair servers working at different speeds. The problem of optimal allocation of failed machines between the servers is examined. The optimal control policy is calculated versus cost structures. As a result the optimal policy can be of threshold type, hysteretic type or have more complicated form. It is shown that the corresponding Markov process for hysteretic control policy belongs to the class of the Quasi-Birth-and-Death processes (QBD) with three diagonal block infinitesimal matrix. The stationary characteristics in this case are derived in matrix analytic form. Some numerical results are used to illustrate a number of features of the controlled model under study.

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References

  1. Artalejo, J.R., Economou, A.: Markovian controllable queueing systems with hysteretic policies: Busy period and waiting time analysis. Method. and Comp. in App. Prob. 7, 353–378 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Falin, G.I.: A multiserver retrial queue with a finite number of sources of primary calls. Math. and Comp. Mod. 20, 33–49 (1999)

    Article  MathSciNet  Google Scholar 

  3. Howard, R.: Dynamic Programming and Markov Processes. Wiley Series, New York (1960)

    MATH  Google Scholar 

  4. Mitrani, I.: Managing performance and power consumption in a server farm. Ann. Oper. Res. 202, 121–134 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  5. Nobel, R., Tijms, H.C.: Optimal control of a queueing system with heterogeneous servers and set-up costs. IEEE Transactions on Automation Control 45(4), 780–784 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Le Ny, L.M., Tuffin, B.: A simple analysis of heterogeneous multi-server threshold queues with hysteresis. In: Proceedings of Applied Telecommunication Symposium (ATS) (2002)

    Google Scholar 

  7. Puterman, M.L.: Markov Decision Process: Discrete Stochastic Dynamic Programming. John Wiley&Sons, New-York (1994)

    Book  MATH  Google Scholar 

  8. Tijms, H.C.: Stochastic Models. An Algorithmic Approach. John Wiley&Sons, New-York (1994)

    MATH  Google Scholar 

  9. Roszik, J., Sztrik, J.: Performance analysis of finite-source retrial queues with nonreliable heterogeneous servers. J. of Math. Sciences 146, 6033–6038 (2007)

    Article  MathSciNet  Google Scholar 

  10. Rykov, V., Efrosinin, D.: On the slow server problem. Autom. and Rem. Control 70(12), 2013–2023 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Johannes Kepler University Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Dmitry Efrosinin & Christopher Spannring

  2. University of Debrecen, Egyetem ter 1, 4032, Debrecen, Hungary

    Janos Sztrik

Authors
  1. Dmitry Efrosinin
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  2. Christopher Spannring
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  3. Janos Sztrik
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, 220030, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kemerovo State University, Anzhero-Sudzhensk, Russia

    Rafael Yakupov

  4. National Research Tomsk State University, 634050, Tomsk, Russia

    Alexander Gortsev

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© 2014 Springer International Publishing Switzerland

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Efrosinin, D., Spannring, C., Sztrik, J. (2014). Optimal Allocation Problem in the Machine Repairman System with Heterogeneous Servers. In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds) Information Technologies and Mathematical Modelling. ITMM 2014. Communications in Computer and Information Science, vol 487. Springer, Cham. https://doi.org/10.1007/978-3-319-13671-4_14

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  • DOI: https://doi.org/10.1007/978-3-319-13671-4_14

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13670-7

  • Online ISBN: 978-3-319-13671-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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