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The achievable region approach to the optimal control of stochastic systems

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  • Marcus Dacre
  • Kevin Glazebrook
  • José Niño-Mora

Abstract

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances (the achievable region) of the system of interest, and (ii) optimising the overall system-wide performance objective over this space. This is radically different from conventional formulations based on dynamic programming. The approach is explained with reference to a simple two-class queueing system. Powerful new methodologies due to the authors and co-workers are deployed to analyse a general multiclass queueing system with parallel servers and then to develop an approach to optimal load distribution across a network of interconnected stations. Finally, the approach is used for the first time to analyse a class of intensity control problems.

Suggested Citation

  • Marcus Dacre & Kevin Glazebrook & José Niño-Mora, 1998. "The achievable region approach to the optimal control of stochastic systems," Economics Working Papers 306, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:306
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    References listed on IDEAS

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    1. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. J. George Shanthikumar & David D. Yao, 1992. "Multiclass Queueing Systems: Polymatroidal Structure and Optimal Scheduling Control," Operations Research, INFORMS, vol. 40(3-supplem), pages 293-299, June.
    3. Gideon Weiss, 1992. "Turnpike Optimality of Smith's Rule in Parallel Machines Stochastic Scheduling," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 255-270, May.
    4. R. Garbe & K. D. Glazebrook, 1998. "Submodular Returns and Greedy Heuristics for Queueing Scheduling Problems," Operations Research, INFORMS, vol. 46(3), pages 336-346, June.
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    More about this item

    Keywords

    Achievable region; Gittins index; linear programming; load balancing; multi-class queueing systems; performance space; stochastic optimisation threshold policy;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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