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Heavy Traffic and Singular Control Problems: Examples and Markov Chain Approximations

  • Harold J. Kushner
  • Paul Dupuis
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 24)

Abstract

Many of the process models which are used for purposes of analysis or control are approximations to the true physical model. Perhaps the dimension of the actual physical model is very high, or it might be difficult to define a manageable controlled dynamical (Markov) system model which describes well the quantities of basic interest. Sometimes the sheer size of the problem and the nature of the interactions of the component effects allows a good approximation to be made, in the sense that some form of the central limit theorem might be used to “summarize” or “aggregate” many of the random influences and provide a good description of the quantities of interest. Because these simpler or aggregate models will be used in an optimization problem, we need to be sure that optimal or nearly optimal controls (and the minimum value function, respectively) for the aggregated problem will also be nearly optimal for the actual physical problem (and a good approximation to the associated minimum value function, respectively).

Keywords

Heavy Traffic Reflection Direction Singular Control Prior Assignment Service Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Harold J. Kushner
    • 1
  • Paul Dupuis
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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