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The achievable region approach to the optimal control of stochastic systems

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  • M. Dacre
  • K. Glazebrook
  • J. Niño‐Mora

Abstract

The achievable region approach seeks solutions to stochastic optimization problems by characterizing the space of all possible performances (the achievable region) of the system of interest and optimizing 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 multi‐class queuing 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

  • M. Dacre & K. Glazebrook & J. Niño‐Mora, 1999. "The achievable region approach to the optimal control of stochastic systems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 747-791.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:4:p:747-791
    DOI: 10.1111/1467-9868.00202
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    Cited by:

    1. José Niño-Mora, 2006. "Restless Bandit Marginal Productivity Indices, Diminishing Returns, and Optimal Control of Make-to-Order/Make-to-Stock M/G/1 Queues," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 50-84, February.
    2. P S Ansell & K D Glazebrook & C Kirkbride, 2003. "Generalised ‘join the shortest queue’ policies for the dynamic routing of jobs to multi-class queues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 379-389, April.
    3. K.D. Glazebrook & C. Kirkbride, 2004. "Index policies for the routing of background jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 856-872, September.
    4. José Niño-Mora, 2000. "Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs," Economics Working Papers 514, Department of Economics and Business, Universitat Pompeu Fabra.
    5. José Niño-Mora, 2000. "On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices," Economics Working Papers 456, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Jasper Vanlerberghe & Tom Maertens & Joris Walraevens & Stijn Vuyst & Herwig Bruneel, 2016. "On the optimization of two-class work-conserving parameterized scheduling policies," 4OR, Springer, vol. 14(3), pages 281-308, September.
    7. Peter Whittle, 2002. "Applied Probability in Great Britain," Operations Research, INFORMS, vol. 50(1), pages 227-239, February.
    8. Vanlerberghe, Jasper & Walraevens, Joris & Maertens, Tom & Bruneel, Herwig, 2018. "Calculation of the performance region of an easy-to-optimize alternative for Generalized Processor Sharing," European Journal of Operational Research, Elsevier, vol. 270(2), pages 625-635.
    9. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    10. Muhammad El-Taha, 2017. "A general workload conservation law with applications to queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 361-381, April.
    11. Sai Rajesh Mahabhashyam & Natarajan Gautam & Soundar R. T. Kumara, 2008. "Resource-Sharing Queueing Systems with Fluid-Flow Traffic," Operations Research, INFORMS, vol. 56(3), pages 728-744, June.
    12. Muhammad El-Taha, 2016. "Invariance of workload in queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 181-192, June.
    13. Esther Frostig & Gideon Weiss, 2016. "Four proofs of Gittins’ multiarmed bandit theorem," Annals of Operations Research, Springer, vol. 241(1), pages 127-165, June.
    14. R. T. Dunn & K. D. Glazebrook, 2004. "Discounted Multiarmed Bandit Problems on a Collection of Machines with Varying Speeds," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 266-279, May.
    15. José Niño-Mora, 1999. "Restless bandits, partial conservation laws and indexability," Economics Working Papers 435, Department of Economics and Business, Universitat Pompeu Fabra.

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