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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. 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.
    3. 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.
    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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