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On structural properties of the value function for an unbounded jump Markov process with an application to a processor sharing retrial queue

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Abstract

The derivation of structural properties for unbounded jump Markov processes cannot be done using standard mathematical tools, since the analysis is hindered due to the fact that the system is not uniformizable. We present a promising technique, a smoothed rate truncation method, to overcome the limitations of standard techniques and allow for the derivation of structural properties. We introduce this technique by application to a processor sharing queue with impatient customers that can retry if they renege. We are interested in structural properties of the value function of the system as a function of the arrival rate.

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References

  1. Blok, H., Spieksma, F.M.: Continuity and ergodicity properties of a parametrised collection of countable Markov processes. Technical report, Leiden University (2013)

  2. Down, D.G., Koole, G.M., Lewis, M.E.: Dynamic control of a single server system with abandonments. Queueing Syst. 69, 63–90 (2011)

    Article  Google Scholar 

  3. Guo, X., Hernández-Lerma, O.: Continuous-Time Markov Decision Processes. Springer, Berlin (2009)

    Book  Google Scholar 

  4. Hordijk, A., Spieksma, F.M.: On ergodicity and recurrence properties of a Markov chain with an application to an open Jackson network. Adv. Appl. Probab. 24, 343–376 (1992)

    Article  Google Scholar 

  5. Koole, G.M.: Monotonicity in Markov reward and decision chains: theory and applications. Found. Trends Stoch. Syst. 1, 1–76 (2006)

    Article  Google Scholar 

  6. Lippman, S.: Applying a new device in the optimization of exponential queuing systems. Oper. Res. 23, 687–709 (1975)

    Article  Google Scholar 

  7. Lund, R.B., Meyn, S.P., Tweedie, L.: Computable exponential convergence rates for stochastically ordered Markov processes. Anna. Appl. Probab. 6(1), 218–237 (1996)

    Article  Google Scholar 

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

    Google Scholar 

  9. Serfozo, R.F.: An equivalence between continuous and discrete time Markov decision processes. Oper. Res. 27(3), 616–620 (1979)

    Article  Google Scholar 

  10. Spieksma, F.M.: Kolmogorov forward equation and explosiveness in countable state Markov processes. Ann. Oper. Res. (2013). doi:10.1007/s10479-012-1262-7

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Authors and Affiliations

  1. Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    S. Bhulai

  2. Department of Economics, Mathematics and Statistics, Birkbeck College, Malet Street, Bloomsbury, London, WC1E 7HX, UK

    A. C. Brooms

  3. Mathematical Institute, University of Leiden, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands

    F. M. Spieksma

Authors
  1. S. Bhulai
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  2. A. C. Brooms
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  3. F. M. Spieksma
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Correspondence to S. Bhulai.

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Bhulai, S., Brooms, A.C. & Spieksma, F.M. On structural properties of the value function for an unbounded jump Markov process with an application to a processor sharing retrial queue. Queueing Syst 76, 425–446 (2014). https://doi.org/10.1007/s11134-013-9371-9

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  • DOI: https://doi.org/10.1007/s11134-013-9371-9

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Mathematics Subject Classification (2000)