IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/435.html
   My bibliography  Save this paper

Restless bandits, partial conservation laws and indexability

Author

Listed:
  • José Niño-Mora

Abstract

We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of linear performance objectives, where the optimal indices are computed by a one-pass adaptive-greedy algorithm, based on Klimov's. We further apply this framework to investigate the indexability property of restless bandits introduced by Whittle, obtaining the following results: (1) we identify a class of restless bandits (PCL-indexable) which are indexable; membership in this class is tested through a single run of the adaptive-greedy algorithm, which also computes the Whittle indices when the test is positive; this provides a tractable sufficient condition for indexability; (2) we further indentify the class of GCL-indexable bandits, which includes classical bandits, having the property that they are indexable under any linear reward objective. The analysis is based on the so-called achievable region method, as the results follow from new linear programming formulations for the problems investigated.

Suggested Citation

  • José Niño-Mora, 1999. "Restless bandits, partial conservation laws and indexability," Economics Working Papers 435, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:435
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/435.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bertsimas, Dimitris. & Niño-Mora, Jose., 1994. "Restless bandit, linear programming relaxations and a primal-dual heuristic," Working papers 3727-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Dimitris Bertsimas & José Niño-Mora, 1996. "Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case," Economics Working Papers 314, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 1998.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Peter Whittle, 2002. "Applied Probability in Great Britain," Operations Research, INFORMS, vol. 50(1), pages 227-239, February.
    8. Dimitris Bertsimas & José Niño-Mora, 1996. "Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case," Economics Working Papers 302, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 1998.
    9. Muhammad El-Taha, 2016. "Invariance of workload in queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 181-192, June.
    10. 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.
    11. Esther Frostig & Gideon Weiss, 2016. "Four proofs of Gittins’ multiarmed bandit theorem," Annals of Operations Research, Springer, vol. 241(1), pages 127-165, June.
    12. 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.
    13. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    14. 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.
    15. Dimitris Bertsimas & José Niño-Mora, 1999. "Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Approach: Part II, The Multi-Station Case," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 331-361, May.
    16. 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.
    17. 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.
    18. 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.

    More about this item

    Keywords

    Stochastic scheduling; Markov decision chains; bandit problems; achievable region;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:435. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.upf.edu/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.