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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Bhulai, S. ; Brooms, Anthony C. ; Spieksma, F.M. (2014)

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.
  • References (10)

    [1] H. Blok and F.M. Spieksma. Continuity and ergodicity properties of a parametrised collection of countable state Markov processes. In preparation, 2013.

    [2] D.G. Down, G.M. Koole, and M.E. Lewis. Dynamic control of a single server system with abandonments. Queueing Systems, 69:63-90, 2011.

    [3] X. Guo and O. HernĀ“andez-Lerma. Continuous-Time Markov Decision Processes. SpringerVerlag Berlin Heidelberg, 2009.

    [4] A. Hordijk and F.M. Spieksma. On ergodicity and recurrence properties of a Markov chain with an application to an open Jackson network. Advances in Applied Probability, 24:343-376, 1992.

    [5] G.M. Koole. Monotonicity in Markov reward and decision chains: Theory and applications. Foundations and Trends in Stochastic Systems, 1:1-76, 2006.

    [6] S. Lippman. Applying a New Device in the Optimization of Exponential Queuing Systems. Operations Research, 23:687-709, 1975.

    [7] R.B. Lund, S.P. Meyn, and L. Tweedie. Computable exponential convergence rates for stochastically ordered Markov processes. Annals of Applied Probability, 6(1):218-237, 1996.

    [8] L.I. Sennott. Stochastic Dynamic Programming and the Control of Queueing Systems. John Wiley & Sons, 1999.

    [9] R.F. Serfozo. An equivalence between continuous and discrete time Markov Decision Processes. Operations Research, 27(3):616-620, 1979.

    [10] F.M. Spieksma. 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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